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Saiiiatt CoUegt libtati 

GEORGE HAYWARD, M.D., 

OF BOSTON. 



a'((r)«*r,i%-')f 



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ELECTRICITY, ELECTROMETER 



MAGNETISM, 



AND 



ELECTROLYSIS. 



BY 

g!^HRYSTAL, M.A., LL.D., 

HONORABT FELLOW OF CORPUS CHRI8TI COLLEGB, CAMBRIDGE ; PROFESSOR OF MATHEMATICS IN THE 

UNIVERAITT OF EDINBURGH ; 



AND 

W. N. SHAW, M.A., F.R.S., 

LKCTURER IN NATUBAL 8CIBM0K AND FBLLOW OF BHMANXrEL COLLBOI, CAMBRIDQB. 



REPRINTED FROM THE NINTH EDITION OF THE ENCYCLOPiEDIA BRITANNICA. 



LONDON: 
ADAM AND CHARLES BLACK. 

1894. 



Ph4'>^:i7^.^tf 






\. 



» : » # 



ELECTRICITY 



ntio- rriHE word Electricity is derived from the Greek word 
h^etioiL J_ ^AcKTpoK, meaning amber. The term was invented 
by Qilbert,^ who used it with reference to the attractions 
and repulsions excited by friction in certain bodie%of which 
amber may be taken as the type. To the cause of these 
forces was given the name Electricity; and out of the 
study of these and kindred phenomena arose the science of 
electricity, of which it is the purpose of the present article 
to give a brief outline. 

The science has been divided into three branches — 
EledrostaticSf which deals with electricity at rest ; Electro- 
kinetics f which considers the passage of electricity from 
place to place ; and Electromagnetism, which treats of the 
relation of electricity to magnetism. We shall, however, 
make no attempt to adhere to this division, but shall 
exhibit the different parts of the subject in such order and 
connection as seems most clear and natural in the present 
state of the science. For the sake of the non-scientific 
reader we prefix a brief history ^ of the science of elec- 
tricity, wherein mention is made of some of the more 
striking electrical discoveries and of the steps by which 
our knowledge of the subject has advanced to its present 
condition. 

Historical Sketch. 

!%>]«•, The name of tbe philosopher who first observed that 
KK) B.O. amber when rubbed possesses the property of attracting 
and repelling light bodies has not been handed down to 
our times. Thales of Miletus is said to have described 
this remarkable property, and both Theophrastus (321 
B.C.) and Pliny (70 a.d.) mention the power of amber to 
attract straws and dry leaves. The same authors speak of 
the lapis lyncuritu, which is supposed to be a mineral 
called tourmaline^ as possessing the same property. The 
electricity of the torpedo was also known to the ancients. 
lAlnul Pliny informs us, that when touched by a spear it para- 
^ lyzes the muscles and arrests the feet, however swift ; and 
^* Aristotle adds that it possesses the power of benumbing 
men, as well as the fishes which serve for its prey. The 
influence of electricity on the human body, and the elec- 
tricity of the human body itself, were also known in 
ancient times. Anthero, a freedman of Tiberius, was 
cured of the gout by the shocks of the torpedo; and 
Wolimer, the king of the Qoths, was able to emit sparks 
115 4.a from his own body. Eustathius, who records this fact, 
also states that a certain philosopher, while dressing and 

' De MagneU Magneiicisque CorporQnu, 

* A portion of tUs historical sketch was written by Sir David 
Brewster, and formed the introduction to his article ** Electricity" 
in last edition of the Bncydopcedia, It has been modified by suppres- 
^ns and alterations here and there, and by large additions at the 
end which were thought necessary to make it suit the present state of 
science, ^or the sake of the student in search of original sources of 
iaformation, pretty copious reference to such has been added through* 
out Valuable for information of this kind the student will find 
Biess's JUilmmifseUctrieUiU, Young's NaiwnU Philosophy, Wiede- 
maim*i OalwsiUsmuSf and the recent work on electricity by Prof. 
Mamrti of tha Coll^ de France, 



undressing, emitted occasionally sudden crackling sparks, 
while at other times flames blaased from him without 
burning his clothes. Such are the scanty gleanings of 
electrical knowledge which we derive from the ancient 
philosophy ; and though several writers of the Middle Ages 
have made occasional references to these facts, and even 
attempted to speculate upon them, yet they added nothing 
to the science, and left an open field for the researches of 
modern philosophers. 

Dr Gilbert of Colchester may be considered as the Oilbart 
founder of the science, as he appears to have been the first (1540- 
philosopher who carefully repeated the observations of the ^^^^^ 
ancients, and applied to them the principles of philosophical 
investigation. In order to determine if other bodies pos- 
sessed the same property as amber, he balanced a light metal- 
lic needle on a pivot, and observed whether or not it was 
affected by causing the excited or rubbed body to approach 
to it. In this way he discovered that the following bodies 
possess the property of attracting light substances : — 
amber, gagates or jet, diamond, sapphire, carbuucle, rock- 
crystal, opal, amethyst, vincentina or Bristol stone, beryl, 
glass, paste for false gems, glass of antimony, slags, 
belemnites, sulphur, gum-mastic, sealing-wax of lac, hard 
resin, arsenic, rock salt, mica, and alum. These various 
bodies attracted, with different degrees of force, not only 
straws and light films, but likewise metals, stones, earths, 
wood, leaves, thick smoke, and all solid and fluid bodies. 
Among the substances which are not excited by friction 
Gilbert enumerated emerald, agate, carnelian, pearls, 
jasper, calcedony, alabaster, porphyry, coral, marble, 
Lydian stone, flints, hematites, smyris (emery or corun- 
dum), bones, ivory, hard woods, such as cedar, ebony, 
juniper, and cypress, metals, and natural magnets. Gilbert 
also discovercMl that the state of the atmosphere affects 
the production of electricity ; dryness with north or east 
wind being a favourable condition, while moisture with 
south wind is unfavourable. An account of Gilbert's 
experiments will be found in his book De Magnete, lib. ii. 
cap. 2. 

Robert Boyle added many new facts to the science Boyle 
of electricity, and he has given a full account of them in (1627- 
his Experiments on the Origin of Electricity, By means of *^^)* 
a suspended needle, he discovered that amber retained its 
attractive virtue after the friction which excited it had 
ceased; and though smoothness of surface had been 
regarded as advantageous for excitation, yet he found a 
diamond which in its rough state exceeded all the polished 
ones and all the electrics which he had tried, having l)een 
able to move a needle three minutes after he had ceased to 
rub it. He found also that heat and tersion (or the clean- 
ing or wiping of any body) increased its susceptibility of 
excitation ; and that if the attracted body were fixed, and 
the attracting body movable, their mutucd approach would 
still take place. To Gilbert's list of '' electrics " Boyle 
added the resinous cake which remained after evaporating 
one-fourth part of good oil of turpentine, the dry mass 
which remains after distilling a mixture of petroleum and 



ELECTRICITY 



[history. 



otto Ton 
Oaericke 
(1602- 
66). 



N«wton 

(164S^- 

1727). 



Hmwks* 

bee, 

1705. 



Stephen 
Gfty 

1736). 



strong spirit of uitre, glass of lead, caput mortuum of 
amber, white sapphire, white amethytst, diaphanous ore 
of lead, camelian, and a green stone supposed to be a 
sapphire. 

To these discoveries of Boyle his contemporary Otto 
von Quericke added the highly important one of electric 
light {Experimenta Nova Magdehurgicaf lib. iv. cap. 15). 
Having cast a globe of sulphur in a glass sphere, and 
broken off the glass, he mounted the sulphur ball upon 
a revolving axis, and excited it by the friction of the hand. 
By this means he discovered that light and sound accom- 
panied strong electrical excitation, and he compares the 
light to that which is exhibited by breaking lump sugar in 
the dark. With this powerful apparatus Quericke verified 
on a greater scale the results obtained bj his predecessors, 
and obtained several new ones of very considerable import- 
ance. He found that a light body, when once attracted 
by an excited electric, was repelled by it, and was in- 
capable of a second attraction until it hfiid been touched by 
some other body ; and that light bodies suspended within 
the sphere of intiuence of an excited electric possessed the 
same properties as if they had been excited. 

To our illustrious countryman Sir Isaac Newton the 
science of electricity owes some important observations. 
He used in his electrical experiments a globe of glass 
rubbed by the hand instead of the sulphur globe of Von 
Quericke. It would appear that Newton was the first to 
use gloM in this way (Optics^ query 8th). We owe also to 
Sir Isaac a beautiful experiment on the excitation of elec- 
tricity which has since become very popular. Having 
fix^ a round disc of glass in a short brass cylinder, 
he placed small pieces of thin paper within the cylinder 
and upon a table, so that the lower surface of the 
glass was one-eighth of an inch distant from the table. 
He then rubbed the upper surface of the glass, and 
he observed the pieces of paper "leap from one part 
of the glass to the other, and twirl about in the air." 
This experiment, after a previous unsuccessful trial, was 
repeated by the Royal Society in 1676 (Brewster's Life 
of Newton^ p. 307). 

Francis Hawksbee, one of the most active experi- 
mental philosophers of his age, added many new facts 
to the science. In 1705 he communicated to the 
Rojral Society several curious experiments on what he 
calls " the mercurial phosphorus." He showed that light 
could be produced by passing conmion air through mer- 
cury placed in a well-exhausted receiver. The air rushing 
through the mercury, blew it up against the sides of the 
glass that held it, '' appearing all around like a body of 
fire, consisting of abundance of glowing globules." The 
phenomenon continued till the receiver was half full of 
air. These phenomena had been observed in the Torricel- 
lian vacuum before Hawksbee's time, and various explana- 
tions suggested. He suspected that they were due to 
electricity, and remarked their resemblance to lightning. 
Like Newton he used a revolving glass globe rubbed by 
the hand to generate electricity. Besides the experiment 
above alluded to he made many others on the electric 
light and on the attractions of electrified bodies. Descrip- 
tions of these will be found in his Physico- Mechanical 
ExperimetUif 1709, and in several memoirs in the Philo- 
iophical Transactions about 1707. 

About the same time Dr Wall (Phil Trans,, 1708) 
observed the spark and crackling sound accompanying the 
electrical excitation of amber, and compared them to 
thunder and lightning. ^ 

One of the most ardent experimentalists of his time 
was Stephen Qray, a Fellow of the Royal Society. 
In his first paper, published in 1720, he showed that 
electricity could be excited by the friction of feathers, 



hair, silk, linen, wooUen, paper, leather, wood, parchment, 
and gold-beaters' skin. Several of these bodies exhibited 
light in the dark, especially after they had been warmed ; 
but all of them attracted light bodies, and sometimes at 
the distance of eight or ten inches. An epoch was made in 
the history of electricity by the discovery of Gray in 1729, 
that certain bodies had, while others had not, the power of 
conveying electricity from one body to another, i.e., in 
modem phrase, conducting it. Gray experimented with a 
glass tube, into the ends of which were fastened two corks ; 
into one of these he fastened a fir rod, and to the end of the 
rod an ivory ball On rubbing the glass he found that the 
ball attracted the light bodies as vigorously as the glass itself. 
He made a variety of experiments with rods of different 
length, and with a packthread, by which he suspended his 
ball from the balcony of an upper story of his house, all 
with the* same result. He then attempted to carry the 
electricity horizontally on a packthread which he suspended 
with hempen strings; but the experiment failed. On 
the occasion of a repetition of the experiments at the 
house of his friend Wheeler, silk strings were suggested 
as a support, and found to answer, while metal wires 
failed. Gray and Wheeler were thus led to the con- 
clusion that it was the material of the supports that 
was in question, and that whereas packthread had, silk 
had not the power of transmitting electricity to a 
distance. Qray and Wheeler managed, by supporting a 
packthread by silk loops, to convey electricity from a 
piece of rubbed glass to a distance of 886 feet. The con- 
ducting power of fluids, and of the human body, was 
established by Qray. He also made many curious experi- 
ments on the electrical properties of resinous cakes, which 
he allowed to cool and harden in the ladles in which they 
had been melted. For an account of these and others the 
student is referred to memoirs in the Philosophical Trans- 
actions for 1731, 1736, &c. 

Desaguliers made many experiments confirming Gray's 
conclusions, and found that bodies that have the property 
of being electrically excitable by friction, or electrics per se, 
have not the power of conduction; whereas conductors are 
not electrics per se. These terms, introduced by him, were 
useful in bringing into concise and scientific language the 
discoveries of Gray. 

While Qray was pursuing his career of discovery in 
England, M. Dufay, of the Academy of Sciences, and su- 
perintendent of the Royal Botanic Gardens, was actively 
employed in the same researches. He found that all bodies, 
whether solid or fluid, could be electrified by an excited 
tube, by setting them on a glass stand slightly warmed, or 
only dried; and that those bodies which are in themselves 
least electrical received the greatest degree of electricity 
from the approach of the glass tube. He repeated the ex- 
periments of Gray, confirming his results, and found that 
electricity was transmitted more easily along packthrea^l 
when it was wetted, and that it might b€ supported upon 
glass tubes in place of silk lines. In this way he conveyed 
it along a string 1256 feet long. He suspended by silken 
strings and electrified a child as Gray had done ; and hav- 
ing suspended himself in a similar manner, he discovered 
that an electrical spark, accompanied with a crackling noise, 
took place when any other person touched him, and he has 
described the prickling sensation like the burning from a 
spark of fire, which is at the same time felt either through 
the clothes or on the skin. The great discovery of Dufay, 
however, was that of two different kinds of electricity. 
He fully recognized the importance of this fundamental 
fact, and gave the name of vitreous electricity to that which 
is produced by exciting glass, rock-crystal, precious stones, 
haur of animals, wool, and many other bodies ; and the name 
of resitious to that which is produced by exciting resinous 



Deiagi 

U«Tt. 



Dufay 
(1699 
1789). 



Vitreo 

and 

resinoi 

elac- 

thdty 



H1BTOST.] 



ELECTRICITY 



bodies, such as amber, copal, gum-lac, silk, paper, thread, 
aod a number of other substances. The characteristic of 
those two electricities was, that a body with vitreous elec- 
tricity attracted all bodies with resinous electricity, and 
repelled all bodies with vitreous electricity; while a body 
with resinous electricity attracted all bodies with vitreous 
electricity, and repelled all bodies with resinous electricity. 
Two electrified silk threads, for example, repel each other, 
and aho two electrified woollen threads, but an electrified 
silk thread will attract an electrified woollen thread. Hence 
it is easy to determine whether any body possesses vitreous 
or resinous electricity. If it attracts an electrified silk 
thread, its electricity will be vitreous ; if it repeU it, it will 
be resinous. 

Qray repeated and vaned the experiments of Dufay, 
and made many new ones. Like Hawksbee and Dr Wall, 
he recognized the similarity between the phenomena of 
electricity and those of thunder and lightning ; and he 
expresses a hope ** that there may be found out a way to 
collect a greater quantity of electric fire, and consequently to 
increase the force of that power, which, by several of these 
experiments, si licet magnis camponere parva, seems to be 
^ the same nature with thunder and lightning,^* 

The discoveries which we have now recounted began to 
^"*^^» rouse the activity of the Qerman and Dutch philosophers. 
To the electrical machine used by Newton and Hawksbee, 
Professor Boze of Wittenberg added the prime conductor, 
which at first consisted of an iron or tin tube supported by 
a man standing upon cakes of rosin ; but it was afterwards 
suspended by silken strings. Professor Winkler of Leipsic 
substituted a cushion in place of the hand for exciting the 
revolving globe ; and Professor Gordon of Erfurt, a Scotch 
Benedictine monk, first used a glass cylinder, eight inches 
long and four broad, which he caused to revolve by means 
of a bow and string. By these means electrical sparks of 
great size and intensity were produced, and by their aid 
various combustible substances, both fluid and solid, were 
inflamed. In 1744 M. Ludolph of Berlin succeeded in 
firing, by the electrical spark, the ethereal spirit of Fro- 
benius. Winkler did the same by a spark from his finger ; 
and he succeeded in inflaming French brandy and other 
weaker spirits after they had been heated. Gordon kindled 
spirits by a jet of electrified water. Dr Miles inflamed 
phosphorus by the electric spark ; and oil, pitch, and 
sealing-wax, when strongly heated, were set on fire by 
similar meansw We refer the student for lists of the works 
of the philosophers just mentioned to the admirable biblio- 
graphy given by Young, Natural Philosophy ^ p. 515. 
itjdiD These striking effects were all produced by the electricity 
W^. obtained immediately from an excited electric ; but a great 
step was now made in the science by the discovery of a 
method of accumulating and preserving electricity iu large 
qaantitiea The author of this great invention is not dis- 
tinctly known ; but there is reason to believe that a monk 
of the name of Kleist, a person of the name of Cuneus, and 
Professor Muschenbroeck of Leyden had each the merit of 
an independent inventor. The invention by which this 
accumulation was effected was called the Leyden Jar or 
Phial^ because it was principally in Leyden that it was 
either invented or tried. Having observed that excited 
electrics soon lost their electricity in the open air, and that 
their loss was accelerated when the atmosphere was charged 
with moisture or other conducting materials, Muschenbroeck 
conceived that the electricity of bodies might be retained 
by surrounding them with bodies which did not conduct it. 
In putting this idea to the test of experiment, he electri- 
fied some water in a glass bottle, and a conmiunication 
having been made between the water and the prime con- 
dofllor, the assistant, who was holding the bottle, on 
tfyiog to disengage the communicating wire, received a 



745' 



sadden shock in his arms and breast, and thus established 
the efi&cacy of the Leyden jar. 

Sir William Watson made some important experiments sir Wd 
at this period of our history (Memoirs in PhU, Trans, WaImd 
about 1747). He succeeded in firing gunpowder by the (^^^~ 
electric spark ; and by mixing the gunpowder with a little 
camphor he discharged a musket by the same power. He 
also fired hydrogen by the electric spark; and he kindled 
both spirits of wine and hydrogen by means of a drop 
of cold water, and even with ice. In the German experi- 
ments the fluid or solid to be inflamed was set on fire by 
an electrified body ; but Sir William Watson placed the 
fluid in the hands of an electrified person, and set it on fire 
by causing a person not electrifieid to touch it with his 
finger. Sir William Watson first observed the flash of 
light which attends the discharge of the Leyden phial, and 
it is to him that we owe the present improved form oif the 
Leyden phial, in which it is coated both without and within 
with tinfoil Dr Bevis indeed had suggested the outside 
coating, and at Smeaton's recommendation, he coated a pane 
of glass on both sides, and within an inch of the edge, with 
tinfoil ; but still the idea of coating the jar doubly belongs 
to Sir William Watson. 

A party of the Royal Society, with the president at their Ezperi 
head, and Sir WiUiam Watson as their chief operator, menta of 
entered upon a series of magnificent experiments, for the ^ 
purpose of determining the velocity of the electric fluid, g^J^^^ 
and the distance to which it could be conveyed. The 
French savans had conveyed the influence of the Leyden 
jar through a circuit of 12,000 feet ; and in one case the 
basin at the Tuileries, containing about an acre of water, 
formed part of the circuit ; but the English philosophers 
made a more complete series of experiments, of which the 
following were the results : — 

1. That in all their operations, when the wires have been properly 
conducted, the electrical commotions from the charged phial nave 
heen very considerable only when the observers at the extremities 
of the wire have touched some substance readily conducting elec- 
tricity with some part of their bodies. 

2. That the electrical commotion is always felt moet sensibly in 
thoee parts of the bodies of the observers which are between the 
conducting wires and the nearest and the most non-electric sub- 
stance, or, in other words, so much of their bodies as comes within 
the electrical circuit. 

3. That on these considerations we infer that the electrical power 
is conducted between these observers by any non-electric substances 
which happen to be situated between them, and contribute to form 
the electncal circuit 

4. That the electrical commotion has been perceptible to two or 
more ohservers at considerable distances from each other, even as 
far as two miles. 

5. That when the observers have been shocked at the end of two 
miles of wire, we infer that the electrical circuit is four miles, viz. 
two miles of wire, and the space of two miles of the non-electrio 
matter between the observers, whether it be water, earth, or both. 

6. That the electrical commotion is equally strong, whether it 'ma 
conducted by water or dry ground. 

7. That if the wires between the electrifying machine and the 
observers are conducted on dry sticks, or other substances non- 
electric in a slight degree only, the effects of the electrical power 
are much greater than when the wires in their prog^ress touch the 
ground, or moist vegetables, or other substances in a great degree 
non-electric. 

8. That by comparing the respective velocities of electricity and 
sound, that of electricity, in any of the distances yet experienced, 
is nearly instantaneous. 

In the following year these experiments were resumed 
with the view of ascertaining the absolute velocity of 
electricity at a certain distance, and it was found *' that 
through the whole length of a wire 12,276 feet the velocity 
of electricity was instantaneous.'' 

The theory of positive and negative electricity which was 
afterwards elaborated by Franklm, was distinctly announced 
by Sir W. Watson. He lays it down as a law that in eleo- 
trical operations there is an afflux of '' electric fluid ** to the 
globe and the conductor, and also an efflux of the same 



6 



ELECTRICITY 



[histost. 



matter from them. In the case of two insulated persons, 
the one in contact with the rubber and the other with the 
conductor, he observed that either of them would communi- 
cate a much stronger spark to the other than to any by- 
stander. The electricity of the one, he says, became more 
rare than it is naturally, and that of the other more dense, 
so that the density of the electricity in the two insulated 
persons differed more than that between either of them and 
a bystander. 

A variety of interesting experiments were made about 
this time by Le Monnier, Nollet, Winckler, Ellicott, 
Jallabert, Boze, Menon, Smeaton, and Miles. In 1746 
Le Monnier confirmed the result previously obtained by 
Oray, that electricity is communicated to homogeneous 
bodies in proportion to their surfaces only. Boze dis- 
covered that capillary tubes which discharged water by 
drops afforded a continuous stream when electrified. The 
' Ahh6 Nollet (Essai sur VElectricUe, 1746; Eecherches, 
1749; LettreSf 1753), the friend and coadjutor of Dufay, 
ascertained that electricity increases the natural evapora- 
tion of fluids, and that the evaporation is hastened by 
placing them in non-electric vessels. Jallabert confirmed 
the result previously obtained by Watson, that electricity 
passes through the substance of a conducting wire, and 
not alqng its surface. Smeaton found that the red hot 
part of an iron bar could be as strongly electrified as the 
cold parts on each side of it. Dr Miles kindled com- 
mon spirits by a stick of black sealing-wax excited by 
dry flannel. Ellicott conceived that the particles of the 
electric fluid repel each other, while they attract those 
of all other bodies. Mowbray concluded that the vege- 
tation of two myrtles was hastened by electrifying them, — 
a result which Nollet confirmed in the case of vegetating 
seeds. The Abb^ Menon found that cats, pigeons, spar- 
rows, and chaffinches lost weight by being electrified 
for five or six hours, and that the same result was true of 
the human body ; and hence it was concluded that electri- 
city augments the insensible perspiration of animals. 
Franklin A high place in the history of electricity must be 
^^' allotted to the name of Dr Benjamin Franklin of Phila- 
delphia. His researches did much to extend our theoreti- 
cal and practical knowledge of electricity, and the clearness 
and vigour of his style made his writings popular, and 
spread the study of the subject. 

One of the first labours of the American philosopher 
was to present, in a more distinct form, the theory of posi- 
tive and negative electricity, which Sir W. Watson had 
been the first to suggest. He showed that electricity is 
not created by friction, but merely collected from its state 
of diffusion through other matter by which it is attracted. 
He asserted that the glass globe, when rubbed, attracted 
the electrical fire, and took it from the rubber, the same 
globe being disposed, when the friction ceases, to give out . 
its electricity to any body which has less. In the case of 
the charged Leyden jar, the inner coating of tinfoil had 
received more than its ordinary quantity of electricity, 
and was therefore electrified positively or f^tis^ while the 
outer coating of tinfoil having had its ordinary quantity of 
electricity diminished, was electrified negatively or minus. 
Hence the cause of the shock and spark when the jar is 
discharged, or when the superabundant plus electricity of 
the inside is transferred by a conducting body to the de- 
fective or minus electricity of the outside. This theory 
of the Leyden phial Franklin established in the clearest 
manner, by showing that the outside and the inside coat- 
ing possessed opposite electricities, and that, in charging 
it, exactly as much electricity is added on one side as is 
subtracted from the other. The abundant discharge of 
electricity by points was observed by Franklin in hia ear- 
liest experiments, and also the power of points to conduct 



90). 



it copiously from an electrified body. Hence he was fur- 
nished with a simple method of collecting electricity 
from other bodies ; and he was thus enabled to perform 
those remarkable experiments which we shall now pro- 
ceed to explain. Hawksbee, Wall, and Nollet had succes- 
sively suggested the similarity between lightning and the 
electric spark, and between the artificial snap and the 
natural thunder. Previous to the year 1750 Franklin 
drew up a statement, in which he showed that all the 
general phenomena and effects which were produced by 
electricity had their counterpart in lightning. After wait- 
ing some time for the erection of a spire at Philadelphia, by 
means of which he thought to bring down the electricity of 
a thunder-storm, he conceived the idea of sending up a kite 
among the clouds themselves. With this view he made a 
small cross of two small light strips of cedar, the arms 
being sufficiently long to reach to the four corners of a 
large thin silk handkerchief when extended. The comers 
of the handkerchief were tied to the extremities of the 
cross, and when the body of the kite was thus formed, a 
tail, loop, and string were added to it. The body was 
made of silk to enable it to bear the violence and wet of a 
thunder-storm. A very sharp pointed wire was fixed at the 
top of the upright stick of the cross, so as to rise a foot or 
more above the wood. A silk ribbon was tied to the end 
of the twine next the hand, and a key suspended at the 
junction of the twine and silk. In company with his son, 
Franklin raised the kite like a common one, in the first 
thunder-storm, which happened in the month of June 1752. 
To keep the silk ribbon dry, he stood within a door, taking 
care that the twine did not touch the frame of the door ; 
and when the thunder-clouds came over the kite he watched 
the state of the string. A cloud passed without any elec- 
trical indications, and he began to despair of success. He 
saw, however, the loose filaments of the twine standing out 
every way, and he found them to be attracted by the ap- 
proach of his finger. The suspended key gave a spark on 
the application of his knuckle, and when the string had be- 
come wet with the rain, the electricity became abundant; 
a Leyden jar was charged at the key, and by the electric 
fire thus obtained spirits were inflamed, and all the other 
electrical experiments performed which had been formerly 
made by excited electrics. In subsequent trials with 
another apparatus, he found that the clouds were some- 
times positively and sometimes negatively electrified, and 
so demonstrated the perfect identity of lightning and elec- 
tricity. Having thus succeeded in drawing the electric fire 
from the clouds, Franklin conceived the idea of protecting 
buildings from lightning by erecting on their highest parts 
pointed iron wire or conductors conmiunicating with the 
ground. The electricity of a hovering or a passing cloud 
would thus be carried off slowly and silently ; and if the 
cloud was highly charged, the lightning would strike in pre- 
ference the elevated conductors. 

The most important of Franklin's electrical writings are 
his Experiments and Observations oti Electricity made at 
Philadelphia, 1751-54 ; his Letters on Electricity, and 
various memoirs and letters, Phil, Trans.^ 1756, 1760, kc 

About the same time that Franklin was making his kite 
experiment in America, D'Alibard and others in France had 
erected a long iron rod at Marli, and obtained results 
agreeing with those of Franklin. Similar investigations 
were pursued by many others, among whom Father Bec- 
caria deserves especial mention. 

These experiments were often dangerous, and in one case DmUi 
a fatal accident occurred. Professor Bichman of St Peters- Wch- 
burg had erected on his house an iron rod to collect the ?»^ 
electricity of thunder-clouds. On the 6th August 1753, 
during a thunder-storm, he was observing, along with his 
friend Sokolow, the indications of an electrometer which 



HIBTORT.J 



ELECTRICITY 



fonned part of his apparatus, when a tremendous thunder- 
clap burst over the neighbourhood. Richman bent to ob- 
serve the electrometer; while in this position, his head 
being a foot from the iron rod, Sokolow saw a globe of 
bluish fire about the size of the fist shoot from the iron rod 
to the professor's head, with a report like that of a pistol. 
The shock was fatal ; Richman fell back upon a chest and 
instantly expired. Sokolow was stupified and benumbed, 
and the red hot fragments of a metallic wire struck his 
clothes, and covered Uiem with burnt marks. 
iton One of the most diligent labourers in the field of electri- 
16' cal science was an Englishman, John Canton {PhU, Trans,, 
1753--54). Before his time it had been assumed as indis- 
putable that the same kind of electricity was invariably pro- 
duced by the friction of the same electric, — ^that glass, for 
example, yielded always vitreous, and amber always resinr 
ous electricity. Having roughened a glass tube by grind- 
ing its surface with emery and sheet lead, he found that it 
possessed vitreous or positive electricity when excited with 
oiled silk, but resinous electricity when excited with new 
flannel. He found, in short, that vitreous or resinous 
electricity might, in certain cases, be developed at will 
in the same tube, by altering the surfaces of the tube 
and the exciting rubber. Removing the polish from one 
half of the tube, he excited the different electricities with 
the same rubber at a single stroke, and, curiously enough, 
the rubber was found to move much more easily over the 
rough than over the polished half. Canton likewise dis- 
covered that glass, amber, sealing-wax, and calcareous 
spar were all electrified positively when taken out of 
mercury ; and hence he was led to the important practical 
discovery that an amalgam of mercury and tin was most 
efficacious in exciting glass when applied to the surface of 
the rubber. Canton discovered, and to a certain extent ex- 
plained by the then prevalent theory of " electrical atmo- 
spheres," the fundamental fact of electrification by induc- 
tion. He also found that the air in a room could be 
electrified positively or negatively, and might remain thus 
electrified for a considerable time, 
mria Beccaria, a celebrated Italian physicist, kept up the 
l<^ spirit of electrical discovery in ItiEdy. He showed that 
water is a very imperfect conductor of electricity, that 
its conducting power is proportional to its quantity, and 
that a small quantity of water opposes a powerful resist- 
ance to the passage of electricity. He succeeded in 
making the electric spark visible in water, by discharging 
shocks through wires that nearly met in tubes filled with 
water. In this experiment the tubes, though sometimes 
eight or ten lines thick, were burst in pieces. Beccaria 
likewise demonsti-ated that air adjacent to an electrified 
body gradually acquired the same electricity, that the 
electricity of the body is diminished by that of the air, and 
that the air parts with its electricity very slowly. He con- 
sidered that there was a mutual repulsion between the 
particles of the electric fluid and those of air, and that in 
the passage of the former through the latter a temporary 
vacuum was formed. Beccaria's experiments on atmosphe- 
rical electricity are of the greatest interest to the meteor- 
ologist For farther account of his work, see his Lettere 
deU* EleUr., 1758; Experimenta, 1772 ; and letters, <fec., 
in PkU. Trans, about 1770. 
mat, The science of electricity owes several practical as well 
rW. as theoretical observations to Robert Symmer (Phil. Trans.^ 
about 1759). In pulling ofl* his stockings in the even- 
ing, he had often remarked that they not only gave a 
orackling noise, but even emitted sparks in the dark. The 
riectricity was most powerful when a silk and a worsted 
■tocking had been worn on the same leg, and it was best 
exhibit^ by putting the hand between the leg and the 
stockings, and pulling them off together. The one stock- 



ing being then drawn out of the other, they appeared more 
or less inflated, and exhibited the attractions and repulsions 
of electrified bodies. Two white silk stockings, or two 
black ones, when put on the same leg and taken off, gave 
no electrical indications. When a black and a white stock- 
ing were put on the same leg, and after ten minutes taken 
off, they were so much inflated when pulled asunder, that 
each showed the entire shape of the leg, and at the dis- 
tance of a foot and a half they rushed to meet each other. 

" But what appears most extraordinary is, that when they are 
separated, and removed at a certain distance from each other, tbeir 
electricity does not appear to have been in the least impaired by 
the shock they had in meeting. They are again inflated, again 
attract and repel, and are as ready to msh together as betore. 
When this experiment is performed with two black stockings in one 
hand, and two white in the other, it exhibits a very curious spectacle; 
the repulsion of those of the same colour, and the attraction of those 
of different colours, throws them into an agitation that is not un- 
entertaining, and makes them catch each at that of its opposite 
colour, at a greater distance than one would expect When allowed 
to come together, they all unite in one mass. When separated, 
they resume their former appearance, and admit of the repetition of 
the experiment as often as you please, till their electricity, gradu- 
ally wasting, stands in need of being recruited. 

Symmer likewise found that a Leyden jar could be 
charged by the stockings either positively or negatively, 
according as the wire from the neck of the jar was pre- 
sented to the black or the white stocking. When the 
electricity of the white stocking was thrown into the jar, 
and then the electricity of the black one, or vice versa, 
the jar was not electrified at all. With the electricity of 
two stockings he charged the jar to such a degree that 
the shock from it reached both his elbows ; and by means 
of the electricity of four silk stockings be kindled spirits 
of wine in a tea-spoon which he held in his hand, and the 
shock was at the same time felt from the elbows to the 
breast. Symmer has the merit of having first maintained 
the theory of two distinct fluids, not independent of each 
other, as Dufay supposed them to be, but co- existent, and, 
by counteracting each other, producing all the pheno- 
mena of electricity. He conceived that when a body is said 
to be positively electrified, it is not simply that it is pos- 
sessed of a larger share of electric matter than in a natural 
state, nor, when it is said to be negatively electrified, of a 
less ; but that, in the former case, it is possessed of a larger 
portion of one kind of electricity, and in the latter, of a 
larger portion of the other ; while a body, in its natural 
stete, remains unelectrified, because there is an equal amount 
of the two everywhere within it. 

Contemporary with Symmer were Delaval, Wilson, 
Cigna, Kinnersley, Wilcke, and Priestley (for the works of 
these electricians consult Young). Delaval found that the 
sides of vessels that were perfect conductors were non- 
conductors, and that animal and vegetable bodies lost their 
conducting power when reduced to ashes. Wilson con- 
cluded that when two electrics are rubbed together, the 
harder of the two is generally electrified positively and 
the other negatively, the electricities always being opposite. 
Cigna made many curious experimente by using silk 
ribbands in place of the silk stockings of Symmer. Kin- 
nersley, the friend of Franklin, made some important 
experiments on the elongation and fusion of iron wires, 
when a strong charge was passed through them in a state 
of tension (Phil. Trans,, 1763); he also experimented 
on the disruptive discharge in air. Wilcke brought to 
light many phenomena respecting the electrification pro- 
duced by the melting of electric substences. 

The pyro-electricity of minerals, or the faculty possessed pyi^ 
by some minerals of becoming electric by heat, and of elee- 
exhibiting negative and positive poles, now began to attract ^^^^^' 
the notice of philosophers. There is reason to believe 
that the lyneurium of the ancients, which, according to 



8 



ELECTRICITY 



[history. 



Theophrastus, attracted light bodies, was the tourmaline^ 
a Ceylon mineral, in which the Dutch had early recog- 
nized the same attractive property, whence it got the 
name of Aschentrikker, or attractor of ashes. In 1717 
M. Lemery exhibited to the Academy of Sciences a stone 
from Ceylon which attracted light bodies ; and Linnaeus, 
in mentioning the experiments of Lemery, gives the stone 
the name of Lapu Mectrictts. The Duke de Noya was 
led in 1758 to purchase some of the stones called tourma- 
line in Holland, and, assisted by Daubenton and Adanson, 
he made a series of experiments with them, a description 
of which was published. The subject, however, had en- 
iSpinus &^^ ^^^ attention of iEpinus, a celebrated German philo- 
(1724- sopher, who published an account of them in 1756. 
1306). Hitherto nothing had been said respecting the necessity 
of heat to excite the tourmaline; but it was shown by 
iEpinus that a temperature between 99 J° and 212° Fahr. 
was requisite for the development of its attractive powers. 
Benjamin Wilson (Phil, Trans. y 1763, &c.), Priestley, and 
Canton continued the investigation; but it was reserved 
for the Abb^ Haiiy to throw a clear light on this curious 
branch of the science (Traits de Mineralogie), He found 
that the electricity of the tourmaline decreased rapidly 
from the summits or poles towards the middle of the 
crystal, where it was imperceptible; and he discovered 
that if a tourmaline is broken into any number of frag- 
ments, each fragment, when excited, has two opposite 
poles. Haiiy discovered the same property in the Siberian 
and Brazilian topaz, borate of magnesia, mesotype, preh- 
nite, sphene, and calamina He also found that the 
polarity which minerals receive from heat has a relation 
to the secondary forms of their crystals, — the tourma- 
line, for example, having its resinous pole at the summit 
of the crystal which has three faces, and its vitreous pole 
at the summit which has six faces. In the other pyro- 
electrical crystals above mentioned, Haiiy detected the 
same deviation from the rules of symmetry in their second- 
ary crystals which occurs in tourmaline. Brard discovered 
that pyro-electricity was a property of the axinite; and 
it was afterwards detected in other minerals. In repeating 
and extending the experiments of Haiiy, Sir David Brewster 
discovered that various artificial salts were pyro-electrical; 
and he mentions tartrate of potash and soda, and tartaric 
acid, as exhibiting this property in a very strong degree. 
He also made many experiments with the tourmaline when 
cut into thin slices, and reduced to the finest powder, 
in which state each particle preserved its pyro-electricity ; 
and he showed that scdezite and mesolite, even when de- 
prived of their water of crystallization and reduced to 
powder, preserve their property of becoming electrical by 
heat. When this white powder is heated and stirred 
about by any substance whatever, it collects in masses like 
new fallen snow, and adheres to the body with which it is 
stirred. (For Sir David Brewster's work on pyro-electricity 
see Trans. R.8.E., 1845; Phil. Mag., Dec. 1847; Edin- 
burgh Journal of Science, Oct. 1824 and 1825). 

In addition to his experiments on the tourmaline, iEpinus 
made several on the electricity of melted sulphur ; and in 
conjunction with Wilcke, he investigated the subject of 
electric atmospheres, and discovered a beautiful method of 
charging a plate of air by suspending large wooden boards 
coated with tin, and having Uieir surfaces near each other 
and parallel iEpinus, however, has been principally 
distinguished by his ingenious theory of electricity, which 
he has explained and illustrated in a separate work (Ten- 
tamen Theorice Electricitatis et Magnetismx) which ap- 
peared at St Petersburg in 1759. This theory is founded 
on the following principles. 1. The particles of the elec- 
tric flnid repel each other with a force decreasing as the 
distance increases. 2. The particles of the electric fluid 



attract the particles of all bodies, and are attracted by 
them, with a force obeying the same law. 3. The electric 
fluid exists in the pores of bodies ; and while it moves 
without any obstruction in non-electrics, such as metals, 
water, kc, it moves with extreme difficulty in electrics, 
such as glass, rosin, dbc. 4. Electrical phenomena are pro- 
duced either by the transference of the fluid from a body 
containing more to one containing less of it, or from its 
attraction and repulsion when no transference takes place. 

The electricity of fishes, like that of minerals, now be- £lee> 
gan to excite very general attention, The ancients, as we *^^ 
have seen, were acquainted with the benumbing power of ^ 
the torpedo, but it was not till 1676 that modem naturalists 
attended to this remarkable property. The Arabians had 
long before given this fish the name of raad or lightning ; 
but Redi was the first who communicated the fact that the 
shock was conveyed to the fisherman by means of the line 
and rod which connected him with the fish. Lorenzini 
published engravings of its electrical organs; Reaumur 
described the electrical properties of the fish ; Kampf er 
compared the effects which it produced to lightning ; but 
Bancroft was the first person who distinctly suspected that 
the effects of the torpedo were electrical In 1773 
Walsh {Phil. Trans., 1773-5) and lugenhousz proved, by 
many curious experiments, that the shock of the torpedo 
was an electrical one; and Hunter (Phil. Trans., 1773-5) 
examined and described the anatomical structure of its 
electrical organs. Humboldt {Ann. de Chim. et de Phys,, i. 
15), Gay-Lussac, and Geoffrey pursued the subject with 
success; and Cavendish (Phil. Trans., 1776) constructed 
an artificial torpedo, by which he imitated the actions of 
the living animal. The subject was also investigated by 
Todd, Sir Humphrey Davy (Phil. Trans., 1829), John 
Davy, and Faraday (Exp. Res., vol ii.). The power of 
giving electric shocks has been discovered also in the 
Gymnotus electricus,^ the Malapterurus electricus,^ the 
Trichiurus electricus,^ and the Tetraodon electricus,^ The 
most interesting and the best known of these singular fishes 
is the Gymnotus or Surinam eel. Humboldt gives a very 
graphic account of the combats which are carried on in 
South America between the gymnoti and the wild horses in 
the vicinity of Calabozo. 

Among the cultivators of electricity Henry Cavendish is Ca^ci 
entitled to a distinguished place. Before he had any^l^j 
knowledge of the theory of iEpinus, he had communicated igio] 
to the Royal Society a similar theory of electrical pheno^ 
mena. As, however, he had carried the theory much further, 
and considered it under a more accurate point of view, 
he did not hesitate to give his paper to the world (Phil. 
Trans., 1771). Cavendish made some accurate experi- 
ments on the relative conducting power of different sub- 
stances. He found that electricity experiences as much 
resistance in passing through a column of water one inch 
long as it does in passing through an iron wire of the 
same diameter 400,000,000 inches long, whence he con- 
cluded that iron wire conducts 400,000,000 times as well 
as rain or distilled water. He found that a solution of 
one part of salt in one of water conducts a hundred times 
better than fresh water, and that a saturated solution of 
sea-salt conducts seven hundred and twenty times better 
than fresh water. Cavendish likewise determined by 
nice experiments that the quantity of electricity on coated 
glass of a certain area increased with the thinness of the 
glass, and that on different coated plates the quantity was 
as the area of the coated surface directly, and as the thick- 
ness of the glass inversely. Although electricity had been 
employed as a chemical agent in the oxidation and fusion 
of metals, yet it is to Cavendish that we owe the first of 
t hose briUiant inquiries which have done so much for the 

> Poweif al s Weak. 



HI8T0RT.] 



ELECTRICITY 



9 



advancement of modem chemistry. By using different 
proportions of oxygen and hydrogen, and examining the 
products which they formed after explosion with the elec- 
tric spark, he obtained a proportion of which the product 
was pure water {PhU, Trans,, 1784-5). The decom- 
position of water by the electric spark was first effected 
Dy Facts Van Troostwijk and Deiman ; improved methods 
of effecting it were discovered and used by Pearson, Cuth- 
bertson, and WoUaston (PAi7. Trans., 1801). 
•wdX The great discovery made by Galvani in 1790, that the 
'^~ contact of metals produced muscular contraction in the frog, 
^ and the invention of the voltaic pile, in 1800, by Volta led 
5. to the recognition of a new kind of electricity called Gal- 
r). vanic or Voltaic Electricity, which is now proved to be 
identical with frictional electricity. The chemical effects of 
the voltaic pile far transcend those of ordinary electricity. 
In 1800 Nicolson and Carlisle discovered the power of 
the pile to decompose water; and in 1807 (Bakerian 
Lecture) Sir Humphry Davy decomposed the earths and the 
alkalies, and thus created a new epoch in the history of 
chemistry, 
lomb Contemporaneous with Cavendish was Coulomb, one of 
'^ the most eminent experimental philosophers of the last 
'' century. In order to determine the law of electrical 
action, he invented an instrument called a torsion balance, 
which has since his time been universally used in all 
deb'cate researches, and which is particularly applicable 
to the measurement of electrical and magnetical actions, 
^pinus and Cavendish had considered the action of elec- 
tricity as diminishing with the distance; but Coulomb 
proved, by a series of elaborate experiments, that it 
varied, like gravity, in the inverse ratio of the square 
of the distance. Dr Robison had previously deter- 
minedi without, however, having published his experi- 
ments, that in the mutual repulsion of two similarly 
electrified spheres, the law was slightly in excess of the 
inverse duplicate ratio of the distance, while in the 
attraction of oppositely electrified spheres the deviation 
from that ratio was in defect ; and hence he con- 
cluded that the law of electrical action was similar to that 
of gravity. Adopting the hypothesis of two fluids. 
Coulomb investigated experimentally and theoretically the 
distribution of electricity on the surface of bodies. He 
determined the law of its distribution between two con- 
ducting bodies in contact ; he measured the density of the 
electricity at different points of two spheres in contact ; he 
ascertained the distribution of electricity among several 
spheres (whether equal or unequal) placed in contact in a 
•traight line ; he measured the distribution of electricity on 
the surface of a cylinder, and its distribution between a 
sphere and cylinder of different lengths but of the same 
diameter. His experiments on the dissipation of electri- 
city possess also a high value. He found that the momen- 
tary dissipation was proportional to the degree of electrifi- 
cation at the time, and that, when the charge was mode- 
rate, its dissipation was not altered in bodies of different 
kinds or shapes. The temperature and pressure of the 
atmosphere did not produce any sensible change ; but be 
concluded that the dissipation was nearly proportional to the 
cube of the quantity of moisture in the air. In examining 
the diBsipation which takes place along imperfectly insu- 
lating substances, he found that a thread of gum-lac was the 
most perfect of all insulators ; that it insulated ten times 
as well as a dry silk thread ; and that a silk thread covered 
with fine sealing-wax insulated as powerfully as gum-lac 
when it had four times its length. He found also that 
the dissipation of electricity along insulators was chiefly 
owing to adhering moisture, but in some measure also to a 
■light conducting power. For the memoirs of Coulomb 
aee Mem. de Math, et Phys. de PAcad, de Sc, 1785, &c. 



Towards the end of the last century a series of experi- 
ments was made by Laplace, Lavoisier, and Volta {Phil. 
Trans,, 1782, or Collezione delV Op,), from which it ap- 
peared that electricity is developed when solid or fluids 
bodies pass into the gaseous state. The bodies which were 
to be evaporated or dissolved were placed upon an insu- 
lating stand, and made to communicate by a chain or wire 
with a Cavallo's electrometer, or with Volta's condenser, 
when it was suspected that the electricity increased gra- 
dually. When sulphuric acid diluted with three parts of 
water was poured upon iron filings, hydrogen was disen- 
gaged with a brisk effervescence ; and at the end of a few 
minutes the condenser was so highly charged as to yield a 
strong spark of negative electricity Similar results were 
obtained when charcoal was burnt on a chafing dish. 
Volta, who happened to be at Paris when these experi- 
ments were made, and who took an active part 
in them, subsequently observed that the electricity 
produced by evaporation was always negative. He 
found that burning charcoal gives out negative electri- 
city ; and in other kinds of combustion he obtained dis- 
tinct electrical indications. In this state of the subject 
Saussure {Voyage dans les Alpes, t. it p. 808, et seqq,) 
undertook a series of elaborate experiments on the electri- 
city of evaporation and combustion. In his first trials he 
found that the electricity was sometimes positive and 
sometimes negative when water was evaporated from a 
heated crucible of iron ; but he afterwards found it to be 
always positive both in an iron and a copper crucible. In 
a silver and a porcelain crucible the electricity was nega- 
tive. The evaporation of alcohol and of ether in a silver 
crucible also gave negative electricity. Saussure made 
many fruitless trials to obtain electricity from combustion, 
and he likewise failed in his attempt to procure it from 
evaporation without ebullition. Many valuable additions 
were about this time made to electrical apparatus, as well 
as to the science itself, by Van Marum, Cavallo, Nicholson, 
Cuthbertson, Brooke, Bennet, Read, Morgan, Henley, and 
Lane ; but these cannot here be noticed in detail 

The application of analysis to electrical phenomena may 
be dated from the commencement of the present century. 
Coulomb had considered only the distribution of electri- 
city on the surface of spheres ; but Laplace undertook to 
investigate its distribution on the surface of ellipsoids of 
revolution, and he showed that the thickness of the coat- 
ing of fluid at the pole was to its thickness at the equator 
as the polar b to the equatorial diameter. Biot (Traite de 
Physique Exp, et Math,) has extended this investigation to 
all spheroids differing little from a sphere, whatever may be 
the irregularity of their figure. He likewise determined 
analytically that the losses of electricity form a geometrical 
progression when the two surfaces of ajar or plate of coated 
glass are discharged by successive contacts ; and he found 
that the same law regulates the discharge when a series of jars 
or plates are placed in communication with each other. It is 
to Poisson {Mem. de VInst, Math, et Phys., 12, 1811, &c.) 
however, that we are mainly indebted for having brought 
the phenomena of electricity under the dominion of analy- 
sis, and placed it on the same level as the more exact 
sciences. Assuming the hypothesis of two fluids, he 
deduced theorems for determining the distribution of 
the electric fluid on the surface of two conducting spheres 
when they are either placed in contact or at any given 
distance. The truth of these theorems had been estab- 
lished by experiments performed by Coulomb long before 
the theorems themselves had been investigated. 

Voltaic electricity had now absorbed the attention of 
experimental philosophers. The splendour of its phe- 
nomena, as well as its association wi^ chemical discovery, 
contributed to give it popularity and importance ; but the 

VIIL — 2 



Laplace, 

La- 

ToiaUr, 

and 

Volta. 



Sana- 
sure. 



Applica- 
tion of 
analysia 
to elec* 
tricity. 



Biot 



PoiiiOD. 



10 



ELECTRICITY 



[hibtobt. 



Magnetic 
action of 
electric 
cnrrent 
dis- 
covered 
by 
Oersted. 



Electro- 
dyna- 
mics. 
Am- 

theory. 



liecent 

progress 

of 

electro- 

dyna- 

ojdcs. 



diBCoreries of Galvaiil and Yolta were destmed, in their 
turn, to pass into the shade, and the intellectual enterprise 
of the natural philosophers of Europe was directed to new 
branches of electrical and magnetical science. Quided by 
theoretical anticipations. Professor H. C. Oersted of Copen- 
liagen {Experimenta drca effectum confliclus electrici in 
acum magneticam) in 1820 discovered that the elec- 
trical current of a galvanic battery, when made to pass 
through a platinum wire, acted upon a compass needle placed 
below the wire. He found that a magnetic needle placed 
in the neighbourhood of an electric current always places 
itself perpendicular to the plane through the current and 
the centre of the needle ; or, more definitely, that a 
magnetic north pole, carried at a constant distance round 
the current in the direction of rotation of an ordinary 
cork-screw advancing in the positive direction of the 
current, would always tend to move in the direction in 
which it is being carried. 

Scarcely had the news of Oersted's discovery reached 
France when a French philosopher, Ampere, set to work to 
develop the important consequences which it involved. 
Physicists had long been looking for the connection be- 
tween magnetism and electricity, and had, perhaps, 
inclined to the view that electricity was somehow to be 
explained as a magnetic phenomenon. It was, in fact, 
under the influence of such ideas that Oersted was led to 
his discovery. Ampere showed that the explanation was 
to be found in an opposite direction. He discovered the 
l)onderomotive action of one electric current on another, 
and by a series of well-chosen experiments he established 
the elementary laws ef electrodynamical action, starting 
from which, by a brilliant train of mathematical analysis, he 
not only evolved the complete explanation of all the electro- 
magnetic phenomena observed before him, but predicted 
many hitherto unknown. The results of his researches 
may be summarized in the statement that an electric current 
in a linear circuit of any form is equivalent in its action, 
whether on magnets or other circuits, to a magnetic shell 
bounded by the circuit, whose strength at every point is 
constant and proportional to the strength of the current. 
By his beautiful theory of molecular currents, he gave a 
theoretical explanation of that connection between electri- 
city and magnetism which had been the dream of previous 
investigators. If wo except the discovery of the laws of 
the induction of electric currents made about ten years 
later by Faraday, no advance in the science of electricity 
can compare for completeness and brilliancy with the work 
of Ampere. Our admiration is equally great whether we 
contemplate the clearness and power of his mathematical 
investigations, the aptness and skill of his experiments, or 
the wonderful rapidity with which he elaborated his dis- 
covery when he had once found the clue. 

In 1821 Faraday, who was destined a little later to do 
30 much for the science of electricity, discovered electro- 
magnetic rotation (Quarterly Journal, xii.), having suc- 
ceeded in causing a horizontal wire carrying a current to 
rotate continuously across the vertical lines of a field of 
magnetic force. The experiment was very soon repeated 
in a variety of forms by De la Rive, Barlow, Ritchie^ 
Sturgeon, and others ; and Davy (Phil, Tratu,), in 1823, 
observed that, when two wires connected with the pole of 
a battery were dipped into a cup of mercury placed on the 
ix)le of a powerful magnet, the fluid metal rotated in op- 
posite directions about the two electrodes. The rotation of a 
magnet about a fixed current and about its own axis was 
at once looked for, and observed by Faraday and others. 
The deflection of the voltaic arc by the magnet had been 
observed by Davy in 1821 (Phil. Trans,); and in 1840 
Walker observed the rotation of the luminous discharge in 
a vacuum tube. For many beautiful experiments on the 



influence of the magnet on the strata, &c., in vacuum tubeSy 
we are indebted to Pliicker, De la Rive, Qrove, Gassiot;, 
and others who followed them. 

One of the first machines in which a continuous motion Eledr 
was produced by means of the repulsions and attractions °^^ 
between electromagnets and fixed magnets or electro- ^°^"^ 
magnets was invented by Ritchie (Phil, Trans, ^ 1833). 
The artifice in such machines consists in reversing the 
polarity of one of the electromagnets when the machine 
is near the position of equilibrium. For a general theory of 
these machines, showing the reasons why they are not 
useful as economic motive powers, see Jacobi (Memoiresur 
V Application de V iHectro-magrietisme au Mouvement des 
Machines, Potsdam, 1835), and Joule (Mech, Mag,, xxxvi.). 
Electro-magnetic engines have, however, found a restricted 
use in scientific workshops, such as Froment's, in driving 
telegraphic apparatus, ka. 

In 1820 Arago (Ann, de Chim, et de Phys,, t zv.) and Magni 
Davy (Annals of Philosophy, 1821) discovered indepcn- "***<>' 
dently the power of the electric current to magnetize iron ^j^^^ 
and steel. Savary (Ann, de Chim, et de Phys., t, xxxiv., cunw 
1827) made some very curious experiments on the alt-er- 
nate directions of magnetization of needles placed at differ- 
ent distances from a wire conveying the discharge of a 
Ley den jar. The dependence of the intensity of magnet- 
ization on the strength of the current was investigated by 
Lenz and Jacobi (Pogg, Ann,, xlvii., 1839), and Joule found 
that magnetization did not increase proportionately with 
the current, but reached a maximum (Sturgeon's Ann, of EL 
iv. 1839). The farther development of this subject, which 
really belongs to magnetism, has been carried on by 
Weber, Miiller, Von Waltenhofen, Dub, Wiedemann, Quin- 
tus Icilius, Riecke, Stoletow, Rowland, and others. The 
use of a core of soft iron, magnetized by a helix surround- 
ing it, has become universal in all kinds of electrical ap- 
paratus. Electromagnets of great power have in this way 
been constructed and used in electrical researches by 
Brewster, Sturgeon, Henry, Faraday, and others. 

The most illustrious among the successors of Ampere was Receni 
Wilhelm Weber. He greatly improved the construction of P^g" 
the galvanometer, and invented the electro-dynamometer, i^l^ 
To these instruments he applied the mirror scale and tele- ^jj^. 
scope method of reading, which had been suggested by mics. 
Poggendorfif, and used by himself and Qauss in magnetic 
measurements about 1833. In 1846 he proceeded with his 
improved apparatus to test the fundamental laws of Am- 
pere. The result of his researches was to establish the 
truth of Ampere's principles, as far as experiments with 
closed circuits could do so, with a degree of accuracy far 
beyond anything attainable with the simple apparatus of 
the original discoverer. The experiments of Weber must be 
looked upon as the true experimental evidence for the theory 
of Ampere, and as such they form one of the corner-stones 
of electrical science. 

While experiment was thus busy, theory waa not idle. In Theof; 
1845 Grassmann published (Pogg. Ann,, Ixiv.) his Neue^^ 
Tluorie der Eledrodynamik, in which he gives an elemen- ®*®*^*'' 
tary law different from that of Ampere, but leading to the j^i^a, 
same results for closed circuits. In the same year F. £. 
Neumann published yet another law. In 1846 Weber 
announced his famous hypothesis connecting electro- 
statical and electrodynamical phenomena. Much has 
been written on the subject by Carl Neumann, Riemann, 
Stefan, Clausius, and others. Very important are three 
memoirs by Helmholtz, in Crelle^s Journal (1870-2-4), in 
which a general view is taken of the whole question, and 
the works of his predecessors are critically handled. We 
shall have occasion, in the body of the article, to refer to 
the dynamical theory of Clerk Maxwell, whidi promLsea 
to effect a revolution in this part of electrical science. 



HI8T0BY.] 



ELECTRICITY 



11 



rmo- By his discovery of thermo-electricity in 1822 {Pogg, 
Ann.^ vi), Seebeck opened up a new department. He 
^^' found that when two different metals are joined in circuit 
there will be an electric current in the circuit if the junctions 
are not at the same temperature ; he arranged the metals 
in a thermo-electric series, just as Volta and his followers 
had arranged them in a contact series. Gumming {Annals 
of PhU,^ 1823) found that the order of the metals was not 
the same at different temperatures. This phenomenon has 
been called thermo-electric inversion. In 1834 Peltier dis- 
covered that if a current be sent round a circuit of two 
metals in the direction in which the thermo-electromotive 
force would naturally send it, then the hot junction is 
cooled, and the cool junction heated. This effect, which is 
reversible, and varies as the strength of the current, is 
called the Peltier effect Sir W. Thomson made many 
experiments on thermo-electricity, and applied to the 
experimental results the laws of the dynamical theory 
of heat His reasonings led him to predict a new 
thermo-electric phenomenon, the actual existence of which 
he afterwards verified by an elabonxtn series of very beau- 
tiful experiments {PhU, Trans., 1856). He hasgiven^a 
general theory of the thermo-electric properties of matter, 
taking into account the effect of structure, &e. His experi- 
mental researches have been ably continued by Professor 
Tait, who, guided by theoretical considerations to the conjec- 
ture that the curves in what Thomson called the " thermo- 
electric diagram"^ must be straight lines, made an extended 
series of experiments, and showed that they were in general 
very approximately either straight lines or made up of 
pieces of straight lines. Our knowledge of thermo-electri- 
city has been advanced by Becquerel, Magnus, Matthiessen, 
Iieroux, Avenarius, and others. Thermo-electric batteries 
of considerable power have been constructed by Markus 
Noe, and Clamond, and employed more or less in the arts, 
rnct- In 1824 Arago (Ann. de Chim, et de Phys,, t. xxvii <fec.) 
of made a remarkable discovery, which led ultimately to re- 
^^' suits of the greatest importance. He found that when a 
magnetic needle is suspended over a rotating copper disc 
the needle tends to follow the motion of the disc This 
phenomenon, which has been called the " magnetism of ro- 
tation," excited great interest ; Barlow {Phil. Trans., 1825), 
Herschel, Seebeck {Pogg. Ann., vii., 1826), and Babbage 
(Phil. Trans., 1825) made elaborate researches on the sub- 
ject; and Poisson {Mem, de VAcad., vii., 1826) attempted 
to give a theoretical explanation in his memoir on magnet- 
ism in motion. The true explanation was not arrived at 
untQ Faraday took up the subject a little later. We may 
mention, here, however, the experiments of Pliicker, 
Matteucci, and Foucault on the damping of the motions of 
masses of metal between the poles of electromagnets. The 
damping of a compass needle suspended over a copper 
plate, observed by Seebeck (/. c), has been taken advan- 
tage of in the construction of galvanometers. 
'^ In 1831 Faraday began, with the discovery of theinduc- 
^Q tion of electric currents, that brilliant series of experi- 
«nti mental researches which has rendered his name immortal. 
»- The first experiment which he describes was made with two 
^' helices of copper wire wound side by side on a block of 
wood, and insulated from each other by intervening layers 
of twine. One of these helices was connected with a gal- 
vanometer, and the other with a battery of a hundred 
plates, and it was found that on making and breaking the 
battery circuit a slight sudden current passed through the 
galvanometer in opposite directions in the two cases. He 
also discovered that the mere approach or removal 
of a circuit carrying a current would induce a current 



^ A mode of repreaentiQg the phenomena of thennD-electricity which 
has been greatly developed and improved by Tait. 



in a neighbouring clgsed circuit, and that the motion 
of magnets produces similar effects. To express in 
a concise manner his discoveries, Faraday invented his 
famous conception of the lines of magnetic force, or lines the 
direction of which at any point of their course coincides with 
that of the magnetic force at that point His discovery can 
be thus stated : — ^Whenever the number of lines of force 
passing through a closed circuit is altered, there is an elec- . 
tromotive force tending to drive a current through the cir- 
cuit, whose direction is such that it would itself produce lines 
of force passing through the circuit in the opposite direction. 
Nothing in the whole history of science is more remarkable 
than the unerring sagacity which enabled Faraday to disen- 
tangle, by purely experimental means, the laws of such a com- 
plicated phenomenon as the induction of electric currents. 
The wonder is only increased when we look to his papers, and 
find the first dated November 1831,^ and another January 
1832, in which he shows that he is in complete possession 
of all the general principles that are yet known on th3 
subject. Faraday very soon was able to show that the 
current developed by induction had all the properties of 
the voltaic current, and he made an elaborate comparison 
of all the different kinds of electricity known, — statical, 
dynamical or voltaic, magneto-, thermo-, and animal elec- 
tricity, — showing that they were identical so far as experi- 
ment could show. In 1833 Lenz made a series of important Law of 
researches {Pogg. Ann., xxxi, 1834, xxxiv., 1835), which, 1«m- 
among other results, led him to his celebrated law by means 
of which the direction of the induced current can be pre- 
dicted from the theory of Ampere, the rule being that the 
direction of the induced current is always such that its 
electromagnetic action tends to oppose the motion which 
produces it. This law leads to the same results as the prin- 
ciples of Faraday. The researches of Ritchie and Henry 
about this time, and of Dove a little later, are also of im- 
portance. In 1845 F. £. Neumann did for magneto- Hathe- 
electric induction what Ampere did for electrodynamics, matical 
by developing from the experimental laws of Lenz the theoty. 
mathc'iatical theory of the subject {Abh. der BerL Akcuk 
der Wiscenschaft, 1845-7). He discovered a function 
which has been called the " potential " (of one linear 
current on another or on itself), from which he deduced 
a theory of induction completely in accordance with ex- 
periment. About the same time Weber deduced the 
mathematical lav7s of induction from his elementary law 
of electrical action, which, as we have already seen, he 
applied to explain electrostatic and electromagnetic action. 
In 1846 Weber, applying his improved instruments, arrived 
at accurate verifications of the laws of induction, which by 
this time had been developed mathematically by Neumann 
and himself. In 1 849 Kirchhoff determined experimentally 
in a certain case the absolute value of the current induced 
by one circuit in another; and in the same year Edlund 
made a scries of careful experiments on the currents of 
self and mutual induction, which led to the firmer estab- 
lishment of the received theories. Helmholtz gave the 
mathematical theory of the course of induced currents in 
various cases, and made a series of valuable experiments in 
verification of his theory {Pogg. Ann., IxxxiiL, 1851). 
Worthy of mention here are also the experiments and 
reasonings of Felici in 1852. In the Philosophical Maga- 
zine for 1855, Sir W. Thomson investigated mathematically 
the discbarge of a Leyden jar through a linear conductor, 
and predicted that under certain circumstances the dis- 
charge would consist of a series of decaying osciUationa. 
This oscillatory discharge was observed in 1857 by Fedder- 
sen {Pogg. Ann., cviiL) The law of Weber has been applied 



• The first experiment seems to have been actually made on the 29th 
August 1831. See Bence Jones's lAfe c/ Faraday^ vol. it p. 1. 



12 



ELECTRICITY 



[histobt. 



by Kirchhoff to the case of conductors in three dimensions. 
The most important of all the recent contribations to this 
part of electrical science is the theory of Clerk Maxwell, 
which aims at deducing the phenomena of the electromag- 
netic field from purely dynamical principles with the aid of 
the fewest possible hypothases {Phil, Trans, , 1864; Elec- 
tricity and Magnetism^ 1873). He has established the gene- 
ral equations which determine the state of the electric field, 
and he has by means of these equations constructed an 
electromagnetic theory of light, which is full of suggestions 
for the philosopher, whether speculative or experimental. 
The theory of Helmholtz, and his valuable criticisms on 
the works of those that have laboured in this department, 
are to be found in three memoirs already alluded to. 
Mag- Magneto-electricity has been largely applied in the arts. 

neto- One of the first machines for producing electricity by 
electrio induction was made by Pixil It consisted of a fixed 
chines, horseshoe armature wound with copper wire, in front of 
which revolved about a vertical axis a horseshoe ma^:- 
net. The machine was furnished with a commutator 
for delivering the alternating currents in a common 
direction. By means of this machine Faraday and 
Hachette decomposed water and collected the disengaged 
gases separately. Many variations of this type of ma- 
chine wore constructed by Ritchie, Saxton, Clark, Von 
Ettingshausen, Stohrer, Dove, Wheatstone, and others. 
In 1857 Siemens effected a great improvement by in- 
venting the form of armature which bears his name. 
The next improvement was to replace the fixed magnets 
by electromagnets, the current for which was furnished 
by a small auxiliary machine. Wilde's machine (1867) 
is of this kind. Siemens, Wheatstone, and others sug- 
gested that the fixed electromagnet should be fed by 
a coil placed on the armature itself, so that starting 
from the residual magnetism of the armature the ma- 
chine goes on increasing its action up to a certain 
point. Ladd's machine (1867) is constructed on this 
principle. The most recent of these machines is that of 
Gramme, the peculiarity of which is that the coil of the 
armature is divided up into a series of coils arranged round 
an axis, the object being to produce a continuous instead 
of a fluctuating current It has been proposed of late to 
employ electromagnetic machines in lighting streets and 
workshops, and the experiment has been tried with some 
success. They have been employed for some time back 
in lighthouse work. The most important inductive appa- 
ratus for the physicist is the induction coil or inducto- 
rium, which has been brought to great perfection in the 
workshop of Ruhmkorff. Poggendorff {Annalen, 1855) 
suggested several improvements in this kind of appa- 
ratus. Fizeau, who added the condenser (1853), Fou- 
cault, who designed the interrupter which bears his name 
(1865), and Ritchie, who devised the plan of dividing 
the coil into sections by insulating partitions, have all 
aided in bringing the instrument to perfection. Very 
powerful machines of this kind have been constructed. A 
large one in the Polytechnic Institution, London, gives a 
29-inch spark, and one recently constructed by Apps for 
Mr Spottiswoode gives a spark of 42 inches. The mathe- 
matical theory of magneto-electric machines has been 
treated by Maxwell {Proc, Roy, Soc, 1867). He has also 
given a theory of the action of the condenser in the induc- 
torinm {Phil, Mag., 1868). Two papers by Strutt (now 
Lord Rayleigh) in PhU, Mag,, 1869-70, are very interest- 
ing in connection with the same subject. 
Ohm's In the year 1827 Dr Q. S. Ohm rendered a great service 
Jaw. to the science of electricity by publishing his mathematical 
theory of the galvanic circuit {Die Galvanische Ketie 
nuUhanatisch hearbeitet). Before his time the quantita- 
tive circumstances of the electric current had been indicated 



in a very vague way by the use of the terms " intensity " £lad 
and " quantity,'* to which no accurately defined meaning "<'**' 
was attached. Ohm's service consisted in introducing and ^ 
defining the accurate notions — electromotive force, current an^ 
strength, and resistance. He indicated the connection of com 
these with experiment, and stated his famous law that the ^^ 
electromotive force divided by the resistance is equal 
to the strength of the current. The theory on which 
Ohm based his law may bo and has been disputed, 
but the law itself and the applications which Ohm and 
others have made of it are in the fullest agreement 
with all known facts. The merit of Ohm really con- 
sists in having satisfactorily analysed a great group of 
phenomena which had up to his time bafi^ed all those who 
attempted the task. How great his service was is easily 
seen when we remark the progress of those who adopted 
his ideas as compared with those who for a time hesitated 
to do so. Ohm was guided in his mathematical work by 
analogy with the problem of the flux of heat, and intro- 
duced for the first time into the theory of the pile, the 
equivalent of the modern word jyotential. Ohm's word was 
eledroscopic force or tension {Spannung), and he showed that 
the fall of the potential is uniform along a homogeneous 
linear conductor. He considered that the potential was 
analogous to the temperature, and the flow of electricity to 
the flow of heat, so that the former just as much as the 
latter obeys the law of continuity. Ohm verified his theo- 
retical conclusions with thermo-electric piles, and he ob- 
served, as Erman {Gilb, Ann,, 1801) had done before him, 
the differences of potential at difl'erent points of the cir- 
cuit. Davy, Pouillet, and Becquerel laboured at the 
experimental verification of Ohm*s law, and a great body 
of evidence was given by Fechner in his Maasbestim- 
mungen fiber die Galvanische Kette (1831). The law of the 
fall of potential was verified by the elder Eohlrausch, who 
employed in his researches Volta's condenser and Dell- 
mann's electrometer {Pogg, Ann,, Ixxv., 1848). Later 
researches of a similar nature were made by Gaugain and 
Branly. Among recent investigations bearing on Ohm's law, 
the most remarkable is the verification for electrolytes by 
Kohlrausch (the younger) and Nippoldt. They principally 
used alternating currents in their researches, which were 
furnished by a " sine inductor," the measuring instI^lment 
employed being the electro-dynamometer of Weber. In 
the report of the British Association for 1876 an account 
is given of some experiments,^ in which the testing of this 
law seems to have been carried to the limit of experimental 
resources. It must now be allowed to rank with the law 
of gravitation and the elementary laws of statical electricity 
as a law of nature in the strictest sense. Many remarkable 
applications of Ohm's law have been made of late, in par- 
ticular to linear conductors by Ohm, Poggendorff", and 
especially Kirchhoff' {Pogg. Ann., 1845-7-8). The works 
of Helmholtz, Smaasen, and Eirchhofi' on conduction in 
three dimensions must also be mentioned. Very import- 
ant, on account of the experimental results with which 
they deal, are the calculations of Du Bois Reymond 
{Pogg., Ixxi, 1845) and Riemann {Werke, Leipsic, 1876) 
on Nobili's rings, and of Kirchhoff* {Pogg., Ixvii., 1848), 
W. R Smith {Proc, Roy. Soc, Edin., 1869-70), Quincke, 
Stefan, Adams, and others on conduction in plates. Theo- 
retical applications to the varying currents in submarine 
cables of great interest have been made by Thomson 
{PhU. Mag,, 1856) and Kirchhoff {Pogg, Ann,, 1857), while 
practical researches of the greatest importance to tele- 
graphy have been made on this and kindred subjects by 
Faraday, Wheatstone, Quillemin, Varley, Jenkin,and others. 
Great improvements in galvanometers and galvanometry 

^ Suggested mainly by Prof. Clerk Maxwell, and carried out by tbe 
present writer. 



[hibtobt. 



ELECTRICITY 



13 



^f' have been made in our time. One of the first to use au 
of electro-magnetic instrument for measuring or indicating 
'^ currents was Schweigger, who in 1820 invented the 
"^ " multiplier." NobiU used (1825) the astatic " multiplier " 
with two needles, which is sometimes named after him. 
Becquerel (1837) used the electromagnetic balance, which 
was employed in an improved form by Lenz and JacobL 
Pouillet invented the sine and tangent compasses (1837). 
The defects of the latter instrument were pointed out by 
PoggendorfiT, and remedies suggested by him as well as 
Wheatstone and others. Weber effected great improve- 
ments in the construction and use of galvanometers, 
adapted them for the measurement of transient currents, 
and elaborated the method of oscillations which had been 
much used by Fechner. In 1849 Helmholtz invented the 
tangent compass with two .coils which bears his name. 
Great improvements in delicacy and promptness of action 
have been made by Sir William Thomson in galvanometers 
destined for the measurement of resistance, and for indi- 
cating the feeble currents of submarine cables. 

The measurement of resistance has been carried to great 
perfection, chiefly owing to the labours of those who have 
re- busied themselves in perfecting the electric telegraph. 
Among such the highest place must be assigned to Sir 
Charles Wheatstone; his memoirs in the Philosophical 
TnuMoctions (1843) gave a great impulse to this depart- 
ment of our science. He invented the rheostat, which 
underwent several modifications, but is now superseded by 
the resistance box which was first used by Siemens. The 
earlier methods of Ohm, Wheatstone, and others for 
measuring resistance were defective, because they de- 
pended on the constancy of the battery which furnished 
the current. These defects are completely obviated in the 
more modern "null methods,'' which may be divided 
into two classes — those which depend on the use of the 
differential galvanometer introduced by Becquerel, and 
those which are modifications of the Wheatstone's bridge 
method, invented by Christie and brought into use by 
Wheatstone. As examples of the latter, we may mention 
the methods of Thomson, and of Matthiessen and Hockin, 
for measuring small resistances, and Thomson's method for 
measuring the resistance of the galvanometer (see Max- 
well's Electricity and Magnetism^ pp. 404, 410), Many 
determinations of the specific resistances of metals and 
alloys have been made by Davy, Ohm, Becquerel, Matthies- 
sen, and others. To Matthiessen in particular science 
is indebted for great improvements in method and a 
large body of valuable results in this department. The 
metals have been arranged in a series according to 
their conducting powers; and this series is found to 
be nearly the same for electricity as for heat The 
conductivity of metals decreases as the temperature in- 
creases, the rate of decrease being nearly the same for 
most pure metals, but much smaller and more variable for 
alloys, which, on the other hand, have in general a large 
specific resistance. The earlier attempts to measure the 
resistance of electrolytes were not satisfactory, owing to 
insufficient allowance for polarization. In later times this 
difficulty has been overcome or avoided, and concordant 
results have been obtained by Beetz, Paalzow, Kohlrausch, 
Nippoldt, and Grotrian. The three last, using the electro- 
dynamometer and sine inductor, have made elaborate re- 
searches, establishing among many other interesting re- 
sults that the conductivity of electrolytes increases with 
the temperature {Pogg. Ann., 1869-74). 
>. The measurement of the electromotive force and that of 
t internal resistance of batteries in action are problems which, 
^ in their most general form, are inextricably connected. It 
Ib easy to measure with considerable accuracy the electro- 
motive force of an open battery. We have merely to 



connect its poles with a Thomson's electrometer, and 
compare the deflection thus obtained with that due to 
some standard electromotive force. Another very satis- 
factory method is Latimer Clarke's modification of Poggen- 
dorff^s compensation method (see MaxweU, 413). It ia 
likewise not difficult to measure by a variety of methods, 
the most satisfactory being that of Mance (Maxwell, 411), 
the internal resistance of a battery when it is only traversed 
by a feeble current But the measurement of the electro- 
motive force and internal resistance of a battery working a 
strong current has hardly as yet been achieved with success; 
not that we undervalue the ingenious and important 
methods of Paalzow, Von Waltenhofen, Beetz (Wiede- 
mann, i § 181), and Siemens {Pogg. Ann,^ 1874). The 
concordant results of the last two are indeed very 
remarkable. Still all these methods are more or less 
affected by the fact that the electromotive force of a 
battery depends on the current which it is sending (see 
Beetz in Pogg, Ann,, cxliL). 

The ''crown of cups" of Yolta was the parent of aBatteriea 
great many other arrangements for the production of 
voltaic electricity. These had for their end either com- 
pactness or diminution of the internal resistance by en- 
larging the plates; we may mention the batteries of 
Cruickshank (1801), Wollaston (1815), and Hare (1822). 
In 1830 Sturgeon introduced the capital improvement 
of amalgamating the zinc plates. In 1840 Smee used 
platinum or silver plates instead of copper ; by platinizing 
these he avoided to a considerable extent polarization by 
adhering hydrogen. In 1836 DanieU invented the two- 
fluid battery which bears his name. This battery is the 
best constant battery hitherto invented, and is, under 
various modifications, largely used in practical and scien- 
tific work. In the same year Qrove invented his well- 
known battery, which surpasses Daniell's in smallness 
of internal resistance and in electromotive force, although, 
on the other hand, it is more troublesome to manage and 
b unsuited for long-continued action. Cooper, in 1840, 
replaced the expensive platinum plates of Grove's battery 
by carbon. This modification was introduced in a prac- 
tical form into the battery of Bunsen (1842), which is 
much used on the Continent, and combines to a certain 
extent the advantages of Qrove and DanielL Among the 
more recent of one-fluid batteries may be mentioned the 
bichromate battery of Bunsen and the L^lanch<S cell. It 
is impossible here even to allude to all the forms of battery 
that have been invented. We may, however, in passing 
notice the gravitation batteries of Meidinger and Varley, 
and the large tray cell of Sir William Thomson. 

Following up the discoveries of Nicholson, Carlisle, Electro. 
Davy, and others, Faraday took up the investigation of ^^"^ 
the chemical decompositions effected by the electric current 
In 1833 he announced his great law of electro-chemical 
equivalents, which made an epoch in the history of this 
part of electricity. He recognized and for the first time 
thoroughly explained the secondary actions which had 
hitherto masked the essential features of the phenomenon. 
Faraday's discovery gave a new measure of the current, 
and he invented an instrument called the voltameter, 
which was much used by those who followed out hia 
discoveries. Space fails us to notice in detail the labours 
of those who verified and developed Faraday's discovery. 
De la Rive, Becquerel, Soret, Buff, Beetz, Hittorf, Mat- 
teucci, DanieU, Miller, and many others have worked in 
this field. 

Many theories of electrolysis have been given. That of Tbeoriei 
Qrutthuss (1805) has been held under various modifi- ^' jj*?" 
cations by many physicists; but none of these theories "^^^"^ 
have done more than give us a convenient mode of repre- 
senting experimental results. Clausius {Pogg, Ann,, 



14 



ELECTKICITY 



[histoby. 



Polariza- 
tion. 



Oontact 
and che- 
mical 
theories 
of the 
pUe. 



Applica- 
tion of 
the prin- 
ciple of 
the con- 
■eiratioi) 
of en- 



cL, 1857) has published a remarkable molecular theory 
of electrolysis, which is free from some of the objections 
to the views of Grotthuss and his followers. 

The advances made in the experimental study of electro- 
lysis reacted on the theory of the galvanic battery. It 
was now recognized that the cause of the inconstancy of 
batteries is the opposing electromotive force due to 
the existence of the products of decomposition at the 
plates of the battery. Qautherot, in 1802, observed the 
polarization current from electrodes which had been used 
for electrolysis. Hitter confirmed his discovery, and con- 
structed on the new principle his secondary pile. Ohm 
abo experimented on this subject. Fechner and Poggen- 
dorff suspected the existence of a transition resistance 
(Uebergangsunderstand) at the places where the chemical 
products were evolved. But the experiments of Lenz, 
Beetz, and others soon showed that a vera causa existed in 
the electromotive force of polarization amply sufficient to 
explain their results. The influence of the strength of the 
current, the size and nature of the plates, time, <S:c., on 
polarization have been investigated by many physicists, 
among whom are prominent Beetz and Poggendorff. 
Determinations of the electromotive force of polarization 
have been made by Daniell, Wheatstone, Poggendorff, 
and Beetz, and recently by Tait and others. Among 
recent labours on polarization are to be mentioned those 
of Helmholtz and his pupils. We must not omit to notice 
here the gas battery of Qrove, and the powerful secondary 
piles which have recently been constructed by Plant6. 
We refer those interested in these and kindred sub- 
jects to the exhaustive accounts in Wiedemann's Gal- 
vanismus. Justice to all contributors to our knowledge is 
impossible in our limited space. 

This Lb perhaps the place to mention the great battle 
that raged so long between the upholders of the two rival 
theories of the action of the pile. Volta and his imme- 
diate successors held that the current was due to the 
electromotive force of contact between the dissimilar 
metals in the circuit, the function of the electrolyte being 
simply to transndt the electricity, there being no contact 
force between metals and liquids. The upholders of the 
chemical theory sought for the origin of the current in the 
chemical affinity between the zinc and the acid 'or their 
equivalents in the battery, and, in the first instance at 
least, denied the existence of the contact force of Volta. 
It was soon shown, however, on the one hand, that there 
wu a contact force between metals and liquids, and, on 
the other, that an electric current could be generated with- 
out a heterogeneous metallic circuit at all. 

Later holders of both theories modified their views as 
experiment established the necessity for so doing. Ohm 
and Fechner and other Continental philosophers inclined 
to a modified contact theory, and Sir William Thomson at 
present lends his weighty authority to that side. On the 
other side are the great names of Faraday, Becquerel, and 
De la Hive. The contact theorists devoted their attention 
more to the electrostatic phenomena of the pile, while the 
chemical theorists studied with great minuteness the 
phenomena of electrolysis, so tbat both theories have 
rendered good service to science. Now-a-days most 
physicists probably recognize too well the defects of both 
theories to think it worth while to attack either, and take 
refuge more or less in eclecticism. 

There was one point which the older adherents of the 
contact theory overlooked, the importance of which was 
more or less dimly perceived by their chemical opponents. 
This was, in modern language, the question, where does the 
energy come from which appears as kinetic energy in the 
movuig parts of electromagnetic engines, as heat in the con- 
dacting wires, through which a current is being driveD^and so 



forth 1 It was not until the dynamical theory of heat had been 
perfected that the first answer to this question was given. 
Joule {PhiL Mag,, 1841) had arrived experimentaBy at JonW 
the law which regulates the generation of heat in conduc- ^^' 
tors by the electric current, and his law was verified by 
Lenz and Becquerel, both for metals and electrolytes. 
Reasoning from Joule's law on the case where the whole of 
the energy appears in the form of heat, Thomson (PhU. 
Mag, J 1851) established the important theorem that the 
electromotive force of an electro-chemical apparatus is, 
in absolute measure, equal to the mechanical equivalent 
of the chemical action on one electro-chemical equivalent of 
the substance. Calculations of the electromotive force of a 
Daniel I's ceU, from the results of Joule, Andrews, and Favre 
and Silbermann,have given numbers agreeing with the direct 
measurements of Bosscha. The total amount of the electro- 
motive force in the circuit having been thus satisfactorily 
determined, the question between the rival theories is re- 
duced to the determination of the seat of this force — At 
which of the junctions does it act ? 

Besides his great services in other branches of electricity, Elect 
Faraday did much to advance electrostatics. His experi- static 
mental investigations on electrostatic induction are of great 
interest, and his discovery of the effect of the medium 
between the electrified bodies opened out a new aspect 
of the phenomenon quite unsuspected by those who held 
too closely to the theories of action at a distance. He 
introduced the term specific inductive capacity, and 
measured the capacity of several solid substances, show- 
ing that in these it was much greater than that of 
air. He conceived that his results were at variance 
with any theory of action at a distance, and gave a theory 
of his own, which accounted for all his facts, and which 
guided him in his investigations. Matteucci and Siemens 
adopted the views of Faraday, and the latter introduced 
refined methods for measuring specific inductive capacities. 
Such measurements have been made in later times by Bar- 
clay and Qibson for paraffin, and by Silow for certain 
fluids. The most remarkable result thus obtained, how- 
ever, are those of Boltzmann, who succeeded not only in 
detecting but in actually measuring the differences between 
the specific inductive capacities of different gases. Faraday 
had looked in vain for such differences, and concluded that 
the specific inductive capacity was the same for all gases. 
The phenomenon of the residual discharge was recognized 
and experimented on by Faraday. KohJrausch, Gaugain, 
Wiillner, and others have also experimented on it; and quite 
recently Mr Hopkinson has obtained some very interesting 
results regarding the superposition of residual discharges. 
These results are analogous to the curious phenomena of 
" elastic recovery" observed by Kohlrausch. 

Sir W. Snow Harris was a very able experimenter, and 
did much to improve electrostatical apparatus. He used 
the electrical balance and the bifilar suspension balance in- 
vented by himself. On the strength of his results he ques- 
tioned the soundness of the views of Coulomb. The work 
of Harris on the influence of the surrounding medium on 
the electric spark is of great importance. Faraday made 
a series of beautiful experiments on this subject, and 
arrived at a body of results which still form a good portion 
of the established facts on this subject. Very important 
in this connection are the measurements of Sir W. Thomson 
of the electromotive force required to produce a spark in 
air between two conductors, which he has found to be dis- 
proportionally smaller for large distances than for small 

The luminous phenomena attending the electric dis- 
charge, especially in vacuum tubes such as those of Qeiss- 
ler, are exceedingly beautiful, and have of late formed a 
favourite subject of experimental study. Many interesting 
results have been obtained, the significance of which we may 



HXffPOET.J 



ELEOTBIOITY 



15 



not yet rightly comprehond. Among the older labours in 
this field we may mention those of Pliicker and Hittorf, De 
la Rire, Riess, Qassiot, and Varley. But even as we write 
our knowledge of the subject is extending, and we refrain 
from referring to more modem results; for historical 
sketching — a difficult task in any case — is unsafe in an open 
field like this, where some apparently insignificant fact may 
contain the germ of a great discovery. We may here 
mention the experiments of Wheatstone on the velocity of 
electricity, valuable less for the results he obtained than 
for the ingenious application of the rotating mirror, then 
used for the first time, which has since been applied with 
much success in the study of the electric discharge. 

One of the greatest names in electrical science is that of 
Riess. In his classical research on the heating of wires by 
the discharge from a battery of Leyden jars, he did for elec- 
tricity of high potential what Joule did for the voltaic 
current The electro-thermometer which he used in these 
researches was an improvement on the older instruments of 
Kinnersley and Harris. Riess repeated and extended the 
experiments of Coulomb, and effected many improvements in 
the apparatus for electrostatical experiments. His Reibungs- 
tledricUdt is a work of great value, and was for long the 
best book of reference open to the experimental student. 
Happily we have now another in the recently published 
work of M. Mascart. 

Sir William Thomson revolutionized experimental elec- 
tricity by introducing instruments of precision. Chief 
among these are his quadrant and absolute electrometers. 
His portable electrometer and water-dropping apparatus are 
instruments of great value to the meteorologist in the study 
of atmospheric electricity, a science which he has done much 
in other ways to forward. Besides this, we owe to him 
many valuable suggestions for electrical apparatus and ex- 
perimental methods, some of which have been carried out 
by his pupils, 
tro- The theory of statical electricity has made great progress 
^ since Poisson's time. Among its successful cultivators we 
^' may mention Murphy {Electricity^ 1833), and Plana (1845). 
The latter went over much the same ground as Poisson, 
extending his results. It was, however, by Qreen {Essay 
on The Application of MathemaiuxU Analysis to the Theories 
of Electricity and Magneiism, 1828 ; or Mathematical 
Papers, edited by N. M. Ferrers), a self-taught mathemati- 
cian, that the greatest advances were made in the mathema- 
tical theory of electricity. " His researches," as Sir William 
Thomson has observed, '< have led to the elementary pro- 
position which must constitute the legitimate foundation of 
every perfect mathematical structure that is to be made 
from the materials furnished in the experimental laws of 
Coulomb. Not only do they afford a natural and complete 
explanation of the beautiful quantitative experiments which 
have been so interesting at all times to practical electri- 
cians, but they suggest to the mathematician the simplest 
and most powerful methods of dealing with problems which, 
if attacked by the mere force of the old analysis, must have 
remained for ever unsolved." One of the simplest appli- 
cations of these theorems was to perfect the theory of the 
Leyden phial, a result which (if we except the peculiar 
acdon of the insulating solid medium, since discovered by 
Faraday) we owe to his geniua He has also shown how 
an infinite number of forms of conductors may be invented, 
so that the distribution of electricity in equilibrium on each 
may be expressible in finite algebraical terms, — an immense 
stride in the science, v»hen we consider that the distribu- 
tion of electricity on a single spherical conductor, an unin- 
fluenced ellipsoidal conductor, and two spheres mutually 
influencing one another, were the only cases solved by 
Poi»on, and indeed the only cases conceived to be solvable 
by mathematical writers. The work of Green, which con- 



tained these fine researches, though published in 1828, 
had escaped the notice not only of foreign, but even of 
British mathematicians ; and it is a singular fact in the 
history of science that all his general theorems were re- 
discovered by Sir William Thomson, Chasles and Sturm, 
and Qauss (see Reprint of Thomson's papers). Sir Wil- 
liam Thomson, however, pushed his researches much 
further than his fellow-labourers. He showed that the 
experimental results of Sir William Snow Harris, which 
their author had supposed to be adverse to the theory oi 
Coulomb, were really in strict accordance with that theory 
in all cases where they were sufficiently simple to be sub- 
mitted to calculation. He was guided in his earlier in- 
vestigations by an analogy between the problems involved 
in steady flux of heat and the equilibrium of electri- 
city on conductors. He showed in 1845 how the pecu- 
liar electric polarization discovered by Faraday in di- 
electrics, or solid insulators subjected to electric force, 
is to be taken into account in the theory of the Leyden 
iar, so as to supply the deficiency in Green's investigations. 
We also owe to Sir William Thomson new synthetical 
methods of great elegance and power. The theory of 
electric images, and the method of electric inversion founded 
thereon, constitute the greatest advance in the mathema- 
tical theory of electrostatics since the famous memoir of 
Green. These he has applied in the happiest manner to 
the demonstration of propositions which had hitherto re- 
quired the resources of the higher analysis, and he has 
sdso found by means of them the distribution on a 
spherical bowl, a case of great interest in the theory of 
partially closed conductors, which had never been attacked 
or even dreamt of as solvable before. The woi^ of 
Professor Clerk Maxwell on Electricity and Magnetism, 
which appeared in 1873, has already exerted great in- 
fluence on the study of electricity both in England and 
on the Continent. In it are fully given his valuable 
theory of the action of the dielectric medium. He regards 
the electrical forces as the result of stress in the meddum, 
and calculates the stress components which will give the 
observed forces, and at the same time account for the 
equilibrium of the medium. The striking discovery re- 
cently made by Mr Kerr of Glasgow, of the eflect 
on polarized light exerted by a piece of glass under 
the action of strong electric force, is of great import- 
ance in connection with Maxwell's theory, and retdizes 
a cherished expectation of Faraday, of whom Maxwell 
is the professed exponent. We must allude here once 
more to Maxwell's electromagnetic theory of light, the 
touchstone of which is the proposition that in transparent 
media, whose magnetic inductive capacity is very nearly 
equal to that of air, the dielectric capacity is equal to 
the square of the index of refraction for light of infinite 
wave length. Although, as perhaps was to be expected, 
owing to disturbing influences such as heterogeneity, this 
proposition has not been found in good agreement with 
experiment in the case of solids, yet for liquids (Silow, 
Pogg. Ann,, civ. clviii.) and gases (Boltzmann, Ibid, 
civ.) the agreement is so good as to lead us to think that 
the theory contains a great part of the whole truth. 

In the earlier stages of the science several units were in- Absolute 
troduced for the measurement of quantities dealt with in «^ti. 
electricity. As examples of these we may mention the 
wire of Jacobi, and the mercury column of Siemens, a metre 
long, with a section of a square millimetre, which at 
given temperatures furnished units of resistance; the 
Darnell's cell, which funushed the unit of electromotive 
force, the chemical unit of current intensity, kc All 
these units were perfectly arbitrary, and there was no con- 
nection of any kind between them. The introdnction of 
a rational system of unitation, based on the fundamental 



16 



ELECTRICITY 



[gensbal phknomhti. 



units of time, mass, and length, was one of the greatest 
steps of onr time. The impulse came from the famous 
memoir of Gauss, Intensiias Vis MagndicoB TerrestrU ad 
Mensuram absolutam revocatct, 1832. In conjunction 
with Weber, he introduced his principles into the measure- 
ment of the earth's magnetic force. To Weber belongs the 
credit of doing a similar service for electricity. He not 
only devised three different systems of such units — the 
electrodynamical, the electrostatical, and the electromag- 
netic — but he carried out a series of measurements which 
practicaUy introduced the last two systems. The funda- 
mental research in this subject is to determine in electro- 
magnetic measure the resistance of some wire from which, 
by comparison, the electromagnetic unit of resistance can 
be constructed. Measurements of this kind were made by 
Kirchhoff in 1849 ; more carefully in two different 
ways by Weber in 1851; by the committee of the Bri- 
tish Association in 1863, &c.; by Kohlrauschin 1870; and 
by Lorenz in 1873. Accounts of these important re- 
searches will be found in Wiedemann and Maxwell, and in 
the collected reports of the British Association on " Elec- 
trical Standards." The ratio of the electrostatic to the 
electromagnetic unit of electric quantity is a velocity (ac- 
cording to Maxwell's electromagnetic theory of light it is 
the velocity of light), the experimental determination of 
which is of the greatest theoretical and practical import- 
ance. Such determinations have been made by Weber and 
Kohlrausch in 1856, by Maxwell in 1868, and by Thom- 
son in 1869. The results are not so concordant as might 
be desired, but the research is a very difficult one. 

For convenience in practice the British Association com- 
mittee have recommended certain multiples of the absolute 
unit, to which they have given names — e.g., the Ohm, the 
Vol^ the Farad, Sic. These have become current to a great 
extent among practical electricians in this country. For 
practical purposes, an empirical standard of electromotive 
force has been introduced by Latimer Clark, whose value 
in volts is given as 1*457. It is very important, in order 
to be able to reduce chemical to absolute measure, to know 
accurately the electro-chemical equivalent of water. Values 
for this hiave been found by Weber (1840), Bunsen (1843), 
Casselman (1843), and Joule (1851). Kohlrausch a873) 
made a careful determination of the electro-chemical equi- 
valent of silver, from which the electro-chemical equivalent 
of water cih be calculated. 

OENEBAL SKETCH OF PnENOMEXA, 

Fondft- If a piece of glass and a piece of sealing-wax be each 
mental rubbed with a dry woollen cloth, it will be found that 
w^J^* both the glass and the wax have acquired the property 
™*" of attracting indiscriminately any small light body in the 
neighbourhood; and it will be further observed, in many 
cases, that the small bodies, after adhering for a little to 
the glass or wax, will be again repelled. 

These actions have at first sight a likeness to the at- 
tractions and repulsions of magnetic bodies, but they are 
sufficiently distinguished from these — 1st, By their origin, — 
being excited by friction and other causes in a great 
variety of bodies, whereas magnetic action is powerfully 
exhibited and communicated only by certain varieties of 
iron and iron ore, by nickel and cobalt, and by certain 
arrangements which we shall have to mention by-and-by; 
2d, By the nature of the bodies acted on; for these 
may be, in the case of excited glass or wax, light particles 
of any substance, whereas the only bodies powerfully acted 
on magnetically are either magnets or their ecpivalents, 
or iron, nickel, and cobalt ; and 3d, By the fact that every 
magnet has two poles possessing opposite properties, whereas 
an electrified body may have similar properties in every 
part of its surface. 



ment. 



If the experiment were carefully tried it would be found 
that a piece of glass excited as above repels another piece 
of glass similarly excited, but attracts an excited piece of 
wax. A convenient way of exhibiting these actions, which 
also brings under our notice another fact of fundamental 
importance, is as follows. Two gilt balls of elder pith are 
fastened to the ends of a light needle of shellac, which 
is balanced horizontally on a point carried on a vertical 
stand (fig. 1). To the stand a stop is fixed for con- 
venience, to prevent the needle b 
from spinning more than half 0^--*.^_^ 

round. If we touch the ball I i — 1 _ A. 

A with a piece of excited 11 ^^^""^ 




away till it is brought up by Fig. 1. 

the stop, while it will, on the other hand, attract B. If, 
again, G be touched with a piece of excited wax, it will 
attract A and repel B. 

Pieces of glass or wax excited in this way are said to be Ddb 
electrified^ and the balls which by contact have acquired ti« 
properties similar to those of the originally electrified bodies ^ 
are said to be electrified by conduction, ^^ 

It appears from the above experiment that the electrifi- dnct 
cations of glass and sealing-wax, when rubbed with wool- 
len, have opposite properties, which they communicate to 
bodies brought mto contact with them. A body which has 
similar electrification to a piece of glass rubbed with wool- 
len is said to be vitreously or positively electrified; a body 
with similar electrification to a piece of sealing-wax rubbed 
with woollen is said to be resinously or negatively electri- 
fied. The result of the above experiment may then be 
summarized thus : — 

Bodies similarly electrified, whether positively or nega- 
tively, repel each other. 

Bodies oppositely electrified attract each other. 

We have seen that a pith ball becomes, by contact with a Con 
positively electrified piece of glass, itself positively electrified. *<>" 
If we take two pith balls, electrify one of them positively, J*° 
and then touch both simultaneously by a piece of thin 
wire, suspended by white silk, and test them with the 
electroscopic needle described above, they will be found 
both positively electrified ; each will repel A and attract 
B, though less powerfuUy than the originally electrified 
ball did, before the connection between them was 
made. The success of the experiment will be found inde- 
pendent of the length or shape of the wire, and will be 
equally good with silver, gold, iron, lead, or any other 
metal. But, if we use a thread of glass or shellac to con- 
nect the balls, the electrification of the first ball will be 
found unaltered, and the second will remain neutral — that 
is, it will not attract or repel another neutral ball, and will 
equally attract both balls, A and B, of the electroscopic 
needle. The difference in the power of transmitting elec- 
trical properties from one body to another, or of aiding in 
electrification by conduction, leads us to divide all sub- 
stances into two classes— conductors, which do very readily, 
and non-conductors, which do not, or do not very readily, 
transmit electrification from one body to another. If we 
connect an electrified conductor by means of another con- 
ductor to a very large conducting body, such as the earth, 
it will be found that so much electrification has been 
carried away from the small body that it is left sen 
sibly neutral If, accordingly, we wish a conducting intc 
body to preserve its electrification unaltered, we must sup- tion 
port it on some non-conducting substance. When thus *"•" 
supported the body is said to be iniulcUed. the non-con- ^"' 



PBOViaiOKAL TBKOBT.] 



ELECTRICITY 



17 




dnctiog support being called the VMulator^ a name which 
has on that account been given to non-conductors gene- 
rally. 

We have remarked above that a neutral pith ball attracts 
equally the positive and negative balls of the electroscopic 
needle ; this leads us to re- 
mark, more explicitly than 
we have hitherto done, that 
an electrified body in general 
and in the first instance 
attracts a neutral or unelec- 
trified body. The explana- 
tion of this action is that 
the originally neutral body 
in presence of the electri 
tied body becomes itself 
electrified for the time. It 
'is said to be electrified 
by induction, and it b 
very easy to show, by 
using large bodies, not only 
that the originally neutral 
body is actually electrified, 
but that it is oppositely 
electrified in different parts. 
Thus (fig. 2) A and B are 
two bodies suitably insu- 
lated and placed one above 
the other. If B be originally 



(3^ 




Fig. 2. 



neutral, and A be positively electrified, then the lower end of 
B will be negatively, and the upper end positively electri- 
fied; as may be easily shown by exploring with a small posi- 
tively electrified pith ball suspended by a dry white silk 
thread ; the little ball will be attracted towards the lower 
end of B, and repelled from the upper. If we remove the 
body A, or, which (as we have seen) amounts to the same 
thing, connect it with the earth, and so " discharge " its 
electrification, we shall find that all traces of electrical ac- 
tion in B have disappeared — i.e., the small positively elec- 
trified pith ball will be attracted everywhere; and, if we 
discharge it too, it will neither be attracted nor repeUed 
anywhere. 

Provisional Theory, 

Before going further into detail, it will be convenient to 
give a working theory of electrical phenomena, so for as 
we have considered them. The use of such a theory at 
the present stage is to enable us to co-ordinate and classify 
the results of experiment, and to furnish a few leading 
principles under which we may group results which 
appear to be due to a common cause. Such a 
theory is invaluable as a memoria technica for experi- 
mental results, and is useful in suggesting directions 
for experimental inquiry; but in framing it we must 
be careful to make it contain as little as possible beyond 
the results of actual experiment, and in using it we must 
be on our guard against allowing it to prepossess our 
minds as to what may be the ultimate explanation of the 
phenomena we are considering. 

Following the caution of Coulomb and the example of 
Sir William Thomson, we shall avoid the use of the term 
electrical fluid, and substitute instead the more succinct and 
of less misleading word electricity. We suppose that a body 
I* which exhibits electrical properties (as above defined) has 
^^"^ associated with its mass a certain quantity of something 
which, without attempting further definition, we shall call 
electricity. Of our right to use the word quantity here we 
shall give experimental justification by-and-by, and then 
the question of the appropriate unit will (vide infra, '' elec- 
tric quantity'') be discussed. We may suppose that elec- 



tricity is distributed throughout the whole mass of a body, 
and speak of electrical " volume density," meaniiig the quan- 
tity of electricity in an element of volume divided by the 
element of volume. We shall also speak of an element of elec- 
tricity, meaning the electricity in an element or very small 
portion of a body. In certain cases we shall find that 
electricity resides on the surface of a body; electrical 
** surface density " then means quantity of electricity on an 
element of surface divided by the element of surface, and 
element of electricity the electricity on an element of 
surface. 

For shortness, we shall denote positive or vitreoua 
electricity by the mathematical sign-f, and resinous or 
negative electricity by the sign-, remarking that the 
choice of the signs is arbitrary, and reserving for the pre- 
sent the question of how far we may associate with these 
signs the corresponding mathematical ideas. 

We shall assume that every element of electricity repels 
every other element of the same sign, and attracts every 
other element of opposite sign. The precise law of thu 
force will be investigated further on 

This force considered as acting on any element of eleo* 
tricity we shall call an electric force. lu perfectly con- 
ducting substances electricity moves with perfect freedom 
under any electromotive force, however smalL In perfect 
non-conducting substances electricity will not move under 
any electromotive force, however great Any case in 
nature lies somewhere between these extremes, but into 
questions of gradation, &c., we do not enter for the present. 

When the forces due to other electrical elements acting 
on the electricity in any element of a body have a resultant, 
that resultant acts on the element itself, and is called the 
ponderomotive force, to distinguish it from the electro- 
motive^ (or electric) force which tends to move -f electri- 
city in one direction and ~ electricity in the opposite- 
direction. 

When a body is neutral, we shall assume that it contains 
eqttal and equally distributed quantities of -I- and - elec- 
tricity, and we shall further suppose those to be practically 
unlimited in amount A -f electrified body is then to be 
conceived as a body which has excess of -f electricity and 
a - electrified body as one which has excess of - electricity. 
Communication of -f electricity to a body is in accordance 
with this to be regarded as equivalent to the abstraction of 
an equal amount of - electricity, and conversely. 

It is easy to see that the above assumptions will explain 
in a general way the phenomena already described. Thus 
the + electricity of the electrified pith ball C acting on the 
•f electricity of the ball A of the electroscopic needle 
repels it, and this force by our assumption is equally 
exerted on the matter of A, therefore A tends to move 
away from C, and will do so as long as it is free to move. 
The action on the - electrified ball B is similarly explained.. 
Conduction and discharge to earth may be explained 
m a similar manner. 

The attraction of an electrified body (-H let U8 sup* 
pose) A on a neutral insulated body B is thus explained. 
The -f electricity on A (fig. 3) attracts the - electri- 
city in B and repels the 
-I- electricity, so that, 
though there is still on the 
whole as much -I- elec- 
tricity as - electricity, yet 
the distribution is no 
longer the same, for, the 
electricity being free to move, the - electricity under the 
attraction approaches A until the non-conducting air 

^ It might be well to om the tenn " electric force '* here, for " elec- 
tromotive force" ia afterwudi naed to mean the line integral of a force 
(see below, p. 24). 

vnL — 3 





Fig. 8. 



18 



ELECTEICITT 



[bLECTBIC dtSASTSn, 



EL 



and the attraction of the separated + electriaitf on B 
Btops it, and the -l- electricity recedes in similar fashion. 
When electrical equilibrinm has been attained the action of 
the + electricity of A on the - electricity of B will exceed 
its action on the + electricity of B, which ia on the whole 
more distant,' the electromotive force on the electricity of 
B will be on the whole attractive, and hence the pondero- 
motive force on B, will be also attractive. 

The above explanation involves of course the general 
Bxplanatiou of electrijkaium by indtidvm. 

ExperimaUal invettigation of Medrkal Quantity, 
Ditlribtttion, and Force. 

In what follows we shall suppose that we have an 
instrument which vrill serve as an electroscope and to 
some extent as an electrometer ; that ia, which shall tell 
us readily whether a body brought into communication 
with it is + or - electrified or not at all, and also enable us 
to tell when one body is more strongly electrified + or - 
than another. 

The gold-leaf electroscope of Bennet or the dry pile 
electroscope of Bohnenberger will meet these require- 
ments, and have been much used in electrical researches. 
We shall, however, suppose that we are using the rudimen- 
tary form of Thomson's electrometer constructed by Elliot 
Brothers for lecture-room experiments, which is new 
much used in England, and answers very well. For a 
description of these and other electroscopes and electro- 
meters, see article Electroueter. 

We shall also assume for the present that we hare the 
means of producing and communicating to any body as 
much of either kind of electrification as we please, and 
pass on to consider the data of experiment regarding the 
distribntion of statical electricity in conducting bodies. 
We are thus at the very outset brought face to face with 
the idea of electric quantity. 

EUctrie QvarUUy. 

We have to explain how the introduction of the term 
quantity into electrical science is justified by experiment, and 
how we can multiply and subdivide quantities of electricity. 
Atthongh it is no doubt possible to introduce the notion of 
quantity independently of the meature of electric force, yet 
the moat convenient and practical mearure of quantity de- 
pends on the measurement of force, and the absolute 
electrostatic unit of quantity is stated in this way. We 
are naturally led, therefore, to combine with the study of 
quantity and distribution the experimental study of the 
laws of electric force. 

We shall have occasion to allude to two leading experi- 
mental methods that have been used in investigating the 
present eubjecL These might be called the old method 
ind the new. 

The old method, which did so much for electrical science 
in the master hand of Coulomb, depended on the use of 
the torsion balance and proof plane, bath invented by 
Coulomb himself. This method was used by Reiss and 
others up to Faraday's time. 

Michell, about Coulomb's time or a little before, first 
suggested the idea of measuring small forces by the torsion 
of a wire. He proposed to apply the method to measure 
- the attraction of gravitation between two bodies of moderate 
size, thus finding the mean density of the earth, and the 
method was actually carried out by Cavendish ; but Cou- 
lomb was in all prohability unaware of Michell's soggestion. 
Ho made careful preliminary experiments (the first of the 
kind) on the torsion of wires, and found that the couple 



required to twist a straight wire through a given ang^ 
varies as the angle of tonioa multiplied by the fourth 
power of the diameter of the wire directly, and as tbe 
length of the wire inversely (Man. dt PAead., 1784). 

'The balance used by Coulomb in most of his ezperimmti 
IS represented in figure 4. 

ABDC is a cylinder of glass 1 toot in diameter and 1 foot hi^ 
This cylinder ia closed by a glass lid pierced centricaUr vcA aooen- 
trically by two apeniiiEs, 
each about 20 lines wide. 
Into the middle opening 
is cemented t gloss tube a 
2 feet high, to the upper 
end of i^ick is fitted a 
torsion head ; the sepa- 
rate parts of the head 
are showa larger at the 
aids of the figure. " 



collar 



;nted to tht 



5 lass tube ; MO a metal 
isc, divided on the edge 
into 360 degrees; thU 
disc is fastened to a tube 
If, which slips into the 
collar H. K ia a button 
vhose neck turns easily 



I '-f 



. hole 



L MOi 



I the 









lower part of the button 
is fastened a small clamp, 
ivliich aeizes the wire of 
the balance. I is an arm 
with a small projecting 
piece wliich slips arer the 
edjp of tho disc 110. •'"'■ <-— Torsion BflJance. 

This piece has a fiilouial mark on it, tvhich enables us to read off tha 
position of the arm on the graduated edge of MO. The horizontal 
arm bd consists of a silk thread or fine straw covered with sealing 
wBi tenoinated by a thread of shellac at 6 about 18 lines long, 
which carries a pith tiall 2 or 8 lines in diameter. At t&s 
other end of tho arm is a vertical disc of oiled paper, which servM 
as a counterijoise to the pith ball, as a liainjier to the osclllatiana, 
and as an indei by means of which the position of tlie horiiontal 
arm can bo read off on a graduation carried round the glass cylinder. 
The eccentric hole in tbe cover of the balance allows the introduc- 
tion of the filed boD a ; this is carried on a shellac stem fastened 
up P, which by means of fiducial marks can be placed in a 
sition on the cover. The H-iro in Coulomb's balance was of 
Sliver, about 30 cm. long. Its diameter was ■003il cm., and it 
weighed about '003 em. He found by the method of oscillations 
that a couple equivalent to the weight of '17 millimmme, actin* 
Bt the end of an arm a decimetre long, would keep the wire twisted 
through 360°. 

Besides this form of balance Coulomb used others, some 
more delicate for electroscopic purposes, and others less so, 
but of larger dimensions, into which he could introduce 
electrified bodies of considerable size. 

Faraday used Coulomb's balance, and Snow Harris used 
the bifilar balance, which is a modification of Coulomb's. 
In the second volume of his £xperimeiUal RaearcAet, 
however, Faraday gives a general method of experiment- 
ing, which to a great extent has superseded the older 
method. This may bo called the " cage method;" it de- 
pends for its success on the use of some delicate instrument 
for measuring difi'erences of potential; this was supplied 
by the quadrant electrometer of Sir William Thomson, 
which has thus completely revolutionized the whole system 
of electrostatic measurement. 

Faraday's experiment was as follows (Exp. Jtes., vol ii. 
p. 279) :— 

Let A (tig. 6) be an insulated hollow conductor with an opeQioK Cage 
to show admission to the interior. Faraday used apewter ice pail!* dmUk 
lOi in. high and 7 in. in diameter Connect the outside of A with 
one electrode of an electrometer E, which may for most purimses be 
the rudimentary *o"n of Thomson's electrometer mentioned above. 
Connect the other electrode of the electrometer with the tartL If 
now we introduce a positively electrified body, say a brass ball C, 



* A Cflindsr of wire gauie will answer squally wall, and attows tha 
experimenter to lea batter what bs is doing. Bach a cylinder w« shall 
oJlforat— .. -.--^ » 



OnnUBITTION.] 



ELECTRICITY 



19 



vie 




niBpended by a white silk striog, we shall find that the electro- 
meter needle is deflected through a certain angle, the spot of light 
going a certain dis- 
tance to the right, sa^, 
of the scale. It will 
be found that, provided 
the ball C is more than 
a certain depth (about 
8 in. in Farady's ex- 
periment) bnlow the 
month of the pail, no 
further motion of the 
ball, right or left, up 
or down, will affect the 
indications of the elec- 
trometer. It will also 
be found that the same 
indications will be got 

to whatever point of Earlb 

the outside of the paiJ Y\tr, 5. 

the electrometer wire *** 

is attached. If we diminish or increase the + electrification of C, 
the electrometer deflection will diminish or increase accordingly. 
If we introduce a negatively electrified ball C, the deflection will 
be to the left, and everything else as before. If C gives a certain 
positive (right) deflection, and Of an equal (left) deflection, then if 
we introduce C and C together, the deflection will be zero. If 
C and C be both + electrified and give equal + deflections, then 
introduced together they will give a double + deflection, and if 
Uiree such balls, all giving equal + deflections, be introduced 
together, they will give a treole + deflection. 

It is obvious that this experiment of Faraday's not only 
gives a very ready test of the electrical state of bodies, but 
at once suggests the notion of electrical quantity, and a 
theoretically possible electrostatic unit. Suppose, in fact, 
we take for our test the deflection of a Thomson's electro- 
meter of given sensibility, then we might specify as a unit 
of electrical quantity the quantity of + electricity on or in a 
brass ball of given size, which will produce with a given 
cage a certain given deflection of the electrometer. 

To make this definition useful we must have the means 
of transferring a given charge from one body to another, 
and charging a body with any multiple or submultiple of 
our unit, and of charging a body with any multiple or sub- 
multiple of the unit of negative electricity, which we may 
define as the quantity of - electricity wluch will just 
annul the action of the unit of + electricity in the electric 
cage. 

All these requirements may bo satisfied by suitably mo- 
difying Faraday's experiment 

We saw that we might move the ball about in the middle 
of our electric cage without affecting the electrometer de- 
flection ; we find, moreover, that when we withdraw the 
electrified ball without touching the cage, the needle returns 
to lero. If, however, before withdrawing the ball we cause 
it to touch the inside of the cage, the electrometer deflec- 
tion remains the same as before, and after the ball has been 
removed the deflection is still the same, while if we examine 
the ball, we find that all traces of electrification have disap- 
peared. 
as- ^ To transfer a giveit quantity of electricity, — If we pn> 
vide ourselves iwith two cages, a large one G, and a 
small one H, and take a ball C, electrified positively with 
unit quantity as above defined, then testing in cage 
O, in connection with the electrometer, we get a certain de- 
flection D. If now we transfer the electrification of C to H, 
by the process just described, and then put H inside G, we 
shall get the same deflection D as before. It appears, 
therefore, that we can transfer electrification from one body 
to another without loss ; we thus fulfil one of our require- 
ments, and give an additional justification of the use of the 
word quantity in the present case. 

To get any multiple or aubmuUiple of the electric unit. — 
We may repeat the process above performed on the small 
case H by touching its inside with the ball C, again electri- 
fied to unit quantity. All the electrification will pass to H 




le 
le 



as before, and if we now test H in Q we shall get a deflec- 
tion 2 D. We can in this way get any multiple we please 
of the unit charge. If we take the elec- 
trified brass ball C and touch it by a per- 
fectly equal neutral ball C, on introducing 
C into G we shall get deflection ^ D; if we 
touch C again by C', previously rendered 
neutral, we shall get deflection ^ D, and so 
on ; if we had touched C simultaneously^ as fc n 

in fig. 6, with two equal neutral balb, we ^* * 

should have got deflection ^ D, and so on. We can thus 
get any submultiple of our unit charge. 

To yet a given multiple and submultiple of the negative 
unit — This is possible when we can get a quantity of — 
electricity, which will just destroy the action of a given 
quantity of + electricity in the electric cage. If we intro- 
duce our given quantity of + electricity into the cage H, 
without allowing the conductor carrying it to touch the 
cage and at the same time put the outside of the cage in 
communication with the ground, then if we remove the 
conductor with the given quantity of + electricity and 
put it in G, it will give the same + deflection as before, 
while H tested in the same way will give a negative deflec- 
tion exactly equal to the former, and if both be introduced 
together there will be no deflection. We can, therefore, 
in this way get a - quantity equal and opposite to a 
given + quantity.^ 

Electrical Distribution, 

Experiments had been made before Coulomb's time to 
determine what effect the nature of a body has on electri- 
cal distribution. Gray and White concluded, from an 
experiment with two cubes of oak, one hollow and the 
other solid, '* that it was the surface of the cubes only 
which attracted." Le Monnier ^ showed that a sheet of 
lead gave a better spark when extended than when rolled 
together. These experiments point to the conclusion that 
electrical distribution in conducting bodies depends merely 
on the shape of the bounding surface. 

We may make experiments confirmatory of this conclu- 
sion with the electric cage. If we electrify a brass sphere 
A, and then touch it with another sphere B, and test the 
electrification of B in the cage, we shall find that the 
amount of electricity taken by B is always the same, what- 
ever its material may be, so long as the radius of its exter- 
nal surface is the same^ Experiment is unable to detect 
any difference in this respect between a solid sphere of 
lead and the thinnest soap-bubble of the same radius. 
Coulomb took a large cylinder of wood, in which he made 
several holes four lines in diameter and four lines deep. 
Having electrified the cylinder and insulated it, he examined 
its electrical condition by means of the proof-plane. This 
instrument, so much used by Coulomb, consisted merely 
of a small disc of gilt paper (in this case a line and a half 
in diameter) fastened to the end of a needle of shellac. 
The disc is applied to any point of a body whose electrifi- 
cation we wish to test so as to be in the tangent plane to 
the surface of the body. Assuming for a moment, what 
we shall by-and-by prove, that electricity resides on the 
surface of bodies, it is natural to suppose that the proof- 
plane, when placed as described, will form part of the 
bounding surface, and will therefore take up as much elec- 
tricity as was originally on the part of the surface which it 

^ The substance of the above and a good deal of what follows is taken 
from Maxweirs Electricity and Magnetism, vol. I. We recommend 
the Rtudent to read his remarks on quantity, § 35, venturing to saggest, 
as an illustration of the transmission of energy by action at a distance, 
the case of two bar magnets, in which the energy of vibration is trane- 
mitted and retransmitted periodically. 8ee Tait's RtcaU Advanass 
in Physical Science, p. 179. 

* Masoart t i. p. 90. 



20 



ELECTRICITY 



[distbibutioh* 



Hollow 
sphere 
experi- 
ment. 



Frank' 
lin's 
experi- 
ment 



Biot'e 

experi' 

men! 



covers. If now we remove the proof-plane in the direction 
of the normal, keeping it, as nearly as possible, parallel to 
the surface, the electricity will not leave it ; but we shall 
carry safely away all that it had when in contact 
with the surface of the body. We may return to the con- 
sideration of the proof-plane when we come' to study 
mathematically the laws of electrical distribution. 

In the experiment with which we are now concerned, 
Coulomb used a very delicate balance (a force of j^ of a 
milligramme was sufficient to keep the wire twisted 
through 90"). When the proof-plane was applied to any 
point of the external surface of the wooden cylinder, and 
then introduced into the torsion balance, it repelled the 
electrified ball of the balance with great force. When it 
was carefully introduced into one of the holes, made to 
touch the bottom, and then carefully withdrawn so as not 
to touch the edge of the hole, it produced no appreciable 
effect on the balance. 

Coulomb varied this experiment as follows. He insu- 
lated and electrified a hollow sphere of metal (fig. 7), and by 
carefully introducing a proof-plane through a small opening 
tested the electrical condition of the interior 
surface. He found no sensible trace of 
electricity inside, except very near the edge 
of the small opening. Hence we conclude 
that if the sphere had been closed entirely 
there would have been no electrification in- 
side. Many experiments have been made 
to .illustrate the proposition that electricity 
resides entirely on the surface of conductors. 
Franklin put a long chain inside a metal 
teapot, which he insulated and electrified. 
When he seized the chain by a hook at the end 
of a glass rod and pulled it out of the teapot 
he observed that a pair of pith balls, suspended side by side 
from the teapot, collapsed more and more as the chain 
was drawn out, and he concluded that the electKfication 
of the teapot, being now spread over a greater surface, had 
become weaker. 

The following experiment of Biot's has become classical. 
A spherical conductor A (fig. 8) is supported on an insulat- 
ing stem D. B and C are 
two hollow hemispheres 
fastened to insulating 
handles E and F. When 
these are fitted together 
they form a sphere some- 
what larger than A, with 
a small hole in it through 
which the stem D can 
pass. If we electrify A 
very strongly, so that 
ifhen put in the electric 
it 
B 




^ 






Pig. 8. 

cage It powerfully deflects the electrometer, and then 
close B and C over A, and make either B or C touch 
it, then separate B and C, and test A, B, and C in the 
cage, we shall find that all the electricity has gone from 
A and spread itself over B and C. 
The following is an ingenious experiment of Faraday's, 





F)g. 9 



involving the same principle. AB (fig. 9) b a wire ring sup- Yme^ 
ported on an insulating stand ; C is a conical muslin bi^ daft 
fitted to the ring with two strings fastened to the vertex of ?«■ 
the cone, giving the experimenter the means of quickly 
turning the bag inside out If the bag be electrified in 
the first position in the figure and tested with the proof- 
plane and electric cage, it will be found that the outside 
only is electrified. If we turn the bag inside out and test it, 
we shall find as befure that what is now the outside, and 
was formerly the inside, is alone electrified. The electricity 
has thus passed through the bag so as to be on the outside 
in both cases. 

Before leaving for a time tne question of the distribution 
of electricity on conductors, it may be well to warn the 
student to accept with due reserve the proposition that 
electricity resides entirely on the surface of conductors, 
and to remind him that such a proposition is from the 
nature of the case incapable of direct experimental proof, 
for we cannot operate in the substance of a mass of metal 
Some of the experiments we have quoted bear more directly 
on the question than others. Coulomb's experiment, 
for instance, shows, strictly speaking, merely that electri- 
city avoids cavities and re-entrant angles. Agein, in Fara- 
da/s experiment with the linen bag, we have not clearly 
defined what we mean by the outside of the body. The 
proposition has on the whole been suggested rather than 
proved. Its meaning will become clearer as we go more 
and more into the theory of distribution,^ and we shall 
meet with it by-and-by as one of the first propositions in 
the mathematical theory. 

Laws of Electric Force. 

Before proceeding to give an account of Coulomb's 
quantitative experiments on electrical distribution, we shall 
describe shortly the methods by which he arrived at the 
laws of electric force, and did for electricity what Newton 
did for astronomy, t.^., laid the foundation for a mathema- 
tical theory of the subject based on the hypothesis of action 
at a distance. 

In this research Coulomb used the form of balance Expe 
which we described above. The clamp holding the fixed m«Qt 
ball of the balance is so adjusted that the centre of the ^^ 
ball falls in a horizontal line through zero of the gradua- ^f ^ 
tion on the glass cylinder and the prolongation of the sus- elemi 
pending wire ; the torsion button is turned till its arm is tary : 
at zero ; the disc, button and all, is then turned till the ^^ '^ 
disc on the arm and the centre of the movable ball are in 
a line with the zero of the lower graduation. The fixed 
ball, which had been removed to allow of the last adjust- 
ment, being replaced, and the movable ball having come to 
rest in contact with it, both are electrified by means of a 
small metal ball carried on an insulating stem of shellac. 
The balls repel each other, and the movable ball takes up 
a certain position of equilibrium ; the corresponding angle* 
is read off. The torsion button is then turned through 
an angle which is noted, so as to bring the balls nearer 
together. The new position of the beam is again read oft ; 
this may be repeated a third time. We are then in pos- 
session of data from which we can draw conclusions as 
to the law of electrical force at different distances. 

Let US assume that the force between two elements of positive 
electricity (supposed collected at two points, technically speaking, 
** regarded as pnysical points ") varies inversely as the square of the 
distance between them. It will be shown in the mathematical 
theory that two spheres Mni/brm/y* electrified, as we shall at present 

^ One additional caution may be useful, viz., not to confound this 
proposition with another of fundamental importance, of which we can 
give direct experimental proof of the most conclusive nature "that 
there is no electrical action inside a hollow conductor containing no 
charged bodies." 

' This condition is not absolutely satisfied in any experiment; it is 
approximately satisfied in Coulomb's experiment. 



£AW or fOBGB.] 



ELECTRICITY 



21 



ftssame the two bails in the balance to be, repel each other, as if 
their electricity were collected at their centres. 

Let c be the angle of equilibrium in any case, r the angle of tor- 
sion. (fig. 10) is the centre of the beam, 
F and M the centres of the fixed and mov- ^ 
able ball (we suppose OF=OM); OK is 

perpendicular to FM. Then FBi> oc sin> ^. 
Hence moment of the force on M about 



Ooc 



osi 
2 

sin'i 



, and the torsonial couple oc r + 1. 




Hence in the three cases the value of (r + c) sin -k^^^-k^^ (^^^ 

must be the same, if the law of the inyerse square agree with the 
exjteriments. 

Coulomb made many experiments of the kind we have 
described. The following is the result which he has 
given of one such : — 





Obttnred. 


CalcnUted. 


Difference. 


T 


f 


f 





126* 
667 


86" 0' 

18 

8 80 


86* 0' 

18 6 

9 4 


• • • 

6* 
84 



The third column is obtained from the two preceding. 
A is calculated by putting r » and f •■ 36° in the formula 



(t + f ) sin 2 tan J - A . 



Then using this value of A and the observed value of r, the 
formula is employed to find f in the two second cases. The 
agreement between the observed and calculated values of c 
is the teat of the truth of the law we have assumed. The 
agreement in the second line is as good as can be expected 
when possible errors of experiment are considered. It will 
be seen, moreover, that the calculated is in excess of the 
observed value, which is what we ought to expect, owing to 
the loss of electricity which goes on during the time con- 
sumed in the experiment That there is such a loss may 
be proved experimentally by simply leaving the movable 
ball to itself after any of the three operations ; it will be 
seen to move slowly towards the fixed ball. We shall re- 
turn hereafter to this loss of electricity, with regard to the 
exact nature of which authorities are not quite agreed.^ 
In the third line the agreement is less good, but here the 
proximity of the balls renders the supposition of unifor- 
mity no longer even approximately allowable. The mutual 
repulsion tends to drive the electricity on each ball farther 
from the other ball, and thus the action between the balls 
is as if the electricity on each were collected at points be- 
yond the centre, so that the observed repulsion must be 
leas than that calculated on the supposition of uniformity 
of distribution. 

Coulomb also made experiments with the torsion balance 
to test whether the law of the inverse square applies 
to the attraction as well as to the repulsion of electrified 
bodies. His experiments confirmed the law ; but the 
difficulty of operating is much greater in this case than 
in the former. He therefore adopted another method 
of experimenting. A small conducting disc was fixed nor- 

^ This is only one of the many experimental difficulties which beset 
the use of the tonuon balance, one of the most difficult of all instru- 
ments to use successfully. To appreciate the skill and sagacity of 
Coulomb in this and other matters, the student must read more de- 
tailed accounts (Riess and Mascart, or Mkmoirtt de VAcad., about 
1785) of his labours than we can give here. He will be richly re- 
paid for his trouble. Nothing is better calculated to rouse the failing 
enthusiasm of the tyro in experimental electricity than a perusal of the 
works of Coulomb, unless it be to read the Bxperimental Researches of 
IWadaj. 



mally on the end of a small shellac needle, which was hung Law of 
up, so as to be horizontal, on a fibre of raw silk attached attrao- 
to a horizontal scale. An insulated conducting globe was ^^?, *^ 
set up with its centre in the same vertical plane as the method^ 
scale, and in the same horizontal plane as the centre of the of osdl. 
small disc. The globe and disc were oppositely electrified, lations. 
and the period of oscillation of the needle was found by 
observing the duration of 15 swings. The time of oscilla- 
tion follows the pendulum law, and varies inversely as 
the square root of the force acting on the needle, hence the 
duration of 15 oscillations will vary inversely as the 
square root of the force, ue, directly as the distance between 
the centres of the globe and disc, if the law of the 
inverse square hold. Coulomb's experiment gave the 
following results : — 



Distance of centres 
of globe and disc 


Daration of 
15 oscUlaUons. 


Ratio of distance 
to daration. 


9 

18 
24 


20 
41 

60 


2-22 
2-28 
2-60 



The numbers in the third column ought to be all equal 
The deviation from equality are not greater than can fairly 
be explained by loss of electricity and errors of observation. 

Coulomb also investigated, both by means of the torsion 
balance and by the method of oscillations, the relation be- 
tween electric force and quantity. 

He electrified the two balls of the torsion balance by 
simultaneous contact with another ball, and observed the 
angle of equilibrium ; he then halved the quantity on the 
fixed ball by touching it with an equal neutral ball, and 
reduced the torsion tUl the angle of equilibrium, and, in 
consequence, the distance between the balls was the same 
as before ; he found the torsional couple in the second case 
to be somewhat less than half what it was in the first. He 
therefore concluded that the force between two elements of 
electricity varies as the product of the quantities. 

Coulomb's experiments were repeated, and his results 
confirmed by Riess,^ and by Mari6-Davy.^ Experiments 
which, when properly interpreted, lead to the same results, 
were made by Snow Harris,* and by Egen.* 

We have then arrived at this general law of electric 
force : — 

If two quantities g, q' of electricity he supposed collected State- 

at two points, whose distance is d. the force between them "^^p* 

aa' of law. 

acts in the straight line Joining the points and cc -^ • 

So far, this law might be merely an approximation to the 
truth. Later on, however, it will be seen to be logically 
deducible from experiments which in delicacy infinitely 
surpass those just described. The law of Coulomb is 
in fact established as certainly as the law of gravitation 
iteelf.« 

By means of the law now given the unit of electrical quan- Defini- 
tity can be defined in a satisfactory and practical manner, tion of 
This unit we now state to be tJiat quantity of positive elec- •J^ol'^t* 
tricity which^ when collected into a pointy repels with unit ^^^ 
of force an equal quantity similarly collected into a point ^nit. 
at unit distance from the former. 

If we take centimetre,' gramme, and second as our 
units of length, mass, and time, the unit force will be that 
force which in a second generates in a gramme of matter 
a velocity of a centimetre per second. 

* Reibwigsdutrieitdi, 6d. L p. 94. * Mascart, i. p. 67. 

* Phil, Trans. J 1834 and 1836. In connection with which we call 
the attention of the student to the classical paper of Sir W. Thomson, 
HeprifU of Papers on BUetrostaHcs and Magnetism^ p. 15 s^ 

* Riess, Bd. i. p. 94. 

* We suppose, of course, that we are dealing always with ant iod 
the same ^electric throughout. 



22 



ELECTRICITY 



[bLXCTRIC DISTSIBDTUOr. 



The law of dertric foree between two quuDtities q and 3' 
now becomes 

Force- -f - 

The unit of quantity which we have just defined itt 
colled the electrostatic unit, in contradistinction to the 
electromagnetic unit which we shall define hereafter. 

Since the dimension of unit of force is [LMT— '], where 
L,M,T symbolize units of length, mass, and time, we hare 
for iko dimension of unit of electrical quantity [Q] 

[q]-[lp']-[l'm't-'1. 

Qaantitaiive Rendte eoncemtng DietribiUion. 
It has already been indicated that electricity in equili- 
brinm resides on the surface of conducting bodies. We must 
now review shortly the experimental method by which this 
surface distribution has been more closely inveetigated. We 
shall stale here some of the general principles arrived at, 
and one or two of the results, reserving others for quota- 
tion when we come to the mathematical theory of electrical 
distribution. 

The most important experiments are due to Conlomb. 
He used the proof-plane and the torsion balance. Riess, 
who afterwards made similar experiments, used methods 
- similar to those of Coulomb. 

Allosion has already been made to the use of the proof- 
plane, and it has been stated that when applied to any part 
of the snrface of an electrified body, it brings away just as 
much electricity as originally occupied the part of the sur- 
face which it covers. If, therefore, we electrify the mov- 
able ball of the torsion balance in the same sense as the 
body we are to exajnine, and note the repulsion caused by 
the proof-plane when introduced in place of the fixed ball 
after having touched in succession two parts of the surface 
of the body, we can, from the iudications of the balance, 
calculate the ratio of the quantities of electricity on the 
plane in the two cases, and hence the ratio of the electrical 
densities at the two points of the surface. We suppose, of 
conne, that the proof-plane is small enough to allow us to 
assume that the electrical density is sensiblynnif ormover the 
smalt area covered by it. In some of his experiments Biess 
used a small sphere (about two lines in diameter) instenil 
of the small disc of the proof-ptane as Conlomb used it. 
The sphere in such cases onght to be very small, and even 
then, except in the case of plane surfaces, its use is objec- 
tionable, unless the object be merely to determine, by twice 
touching the same point of the same coudnctor, the ratio 
of the whole charges on the conductor at two different 
times. The fundamental requisite is that the testing body 
shall, when applied, alter the /orm of the testing body as 
little as possible,^ and this requisite is best satisfied by a 
small disc, and the better the smaller the disc is. The 
theoretically correct procednre would be to have a small 
portion of the actual surface of the body movable. If we 
could remove such a piece so as to break contact with all 
neighbouring portions simultaneously, then we should, 
by testing the electrification of this in the balance, get a 
perfect measure of the mean electric surface density on the 
removed portion. We shall see that Coulomb did employ 
a method like this. 



There are various ways of osing the torsion balance m 
researches on distribution. We may either electrify the 
movable ball independently {as above described), or «e 
may electrify it each time by contact with the proof-plane 
when it is inserted into the balance. It must be noticed 
that the repulsion of the movable ball is in ths first tarn 
proportional to the lAarge on the proof-plane, but in the 
second to the square of the charge, so that the indications 
mnst be reduced differently. 

In measuring we may either bring the movable ball to a 
fixed position, in which case the whole torsion required to 
keep it in this position is proportional to the charge on the 
proof-plane (or to its square, if the second of the above 
modes of operation be adopted), or we may simply olMm 
the angle of equilibrium and calculate the quantity from 
that. It is supposed, for simplicity of explanation in dl 
that follows, that the former of the two altemativea is 
adopted, and that the movable ball is always mdependently 
charged. _ 

The gradual loss of electncity experienced more or less 
by every insulated conductor has already been alluded to. 
This loss forms one of the greatest difficulties to be encoun- 
tered in such experiments as we are now describing If 
we apply the proof-plane to a part of a conductor and take 
the balance reading, giving a torsion r^ say, and repeat the 
observation, after time t, we shall get a different teiaion 
Tg, owing to the loss of electricity in the interval This loss, 
partly if not mainly due to the insulating supports, depends 
on a great many circumstances, some of which are entirely 
beyond even the observation of the experimenter. We may 
admit, however, what experiment confirms within certain 
small limits, that the rate of loss of electricity is propor- 
tional to the charge, and we shall call ^-^^^ (the loss per 
unit of time on hypothesis of uniformity) the coefficient of 
dissipation (S). This coefficient, although, as we have in- 
plied, tolerably constant for one experiment, will vaiy very 
much from experiment to experiment, and from day to 
day ; it depends above all on the weather. 

Supposing we have determined this coefficient by such 
an observation as the above, then we can calculi the 
torsion r, which we should have observed had we touched 
the body at any interval (' after the first experiment; for 
we have, provided f be small, 

T'=.r,-&'-Tj+S{i-C). 
In particular, if ('- J ', we have 

'■-}('■ + '!)• 

Coulomb used this principle in comparing the electric 
densities at two points A and A' of the same conductor. 
He touched the two points a number of times in sncceeaion, 
first A, then A', then A again, and so on, observing the cor- 
responding torsions T|, Tj', T2,Tg',<tc., the intervals between 
the operations being veiy nearly equal. He thus got for 

the ratio of the densities at A and A' the values -^^r* 



' It li grident from what we hiiT« &dvanc«d hen Itut the oia of tli« 
pTOor-jiUiiB to dctermiat ths atectric detiBit; at pointi of i snrfacs 
wh^re the currature ia very great, t.g., at edges or conica] pointi ia 
In a droi a ai ble. If wa attampt to detcrmiae the electrical dsoaltr at the 
veitai of a cona hj applying a proof-aphers there, aa Rlesi did, we 
■hall Tacy sTidentlT get a result tonch under the mark, owing to the | distribution. 
blDBting of the point when the tphere ia im tilu. We ihonld, on the ; proof-plaues may all' be Used 

other hand, lot an oppoiita reaaoa, set too Urn a ninlt bv applv- fi. v * : i_ '■ ■ 

bg a proof -plane rigElS. to a pcSit of a ,Jt!^wb«, th. ciniioi. | t^f ^ ^_^_ ,*'^!y.''' 



_rli_ Zl^tl*, &c. These values oueht to be all 

Ti'-Ht,', St,' ' ° 

equal: the mean of them was taken as the best resolt 

In certain cases, where the rapidity of the electric dissi- 
pation was too great to allow the above method to bo 
applied, Riess used the method of paired proof-planes. For 
a description of this, and for some elaborate calculations 
on the subject of electrical dissipation, the reader is referred 
to RisBs's work. 

The cage method is well adapted for experiments on 
The proof-plane, proof-ephere, or paired 
ised in conjunction with it If 
insualted, and a tolerably deli- 
cate Thomson's electrometer be used, bo that the cage nMy 



OOUU>1Cb'b RBSULT8.] 



ELECTRICITY 



23 



be made large, and the surface density on its oatside there- 
fore small, there will be little loss of the external charge ; 
and the method has this advantage, that dissipation from 
the proof-plane inside the cage does not affect the result of 
the measurement in hand, it being indifferent, qiM effect on 
the electrometer, whether the electricity inside the cage be 
on the proof-plane, in the air, or elsewhere, provided 
merely it be inside. The state of the cage as to electrified 
air, <kc., is easily tested by the electrometer at any time. 

Coulomb's Results, — If we electrify a sphere, and test 
the electrical density at two points of its surface, 
experiment will show, as would be expected from the 
symmetry of the body, that the density at the two 
points is the same. If we test the electric density at 
any point of a sphere, and then halve its charge by 
division with an equal neutral sphere, and test the electric 
density again, we shall find it half what it was before. 
The electric density at any point is^ therefore propor- 
tional to the whole charge on the sphere, or to the mean 
density, meaning by that the whole 'charge divided by the 
whole surface of the sphere. 

If, instead of a sphere, we operate with an ellipsoid 
generated by the revolution of an ellipse about its major 
axis, we shall find that the electric density is not uniform 
as in the case of the sphere, but greater at the sharp ends 
of the major axis than at the equator, and the ratio of the 
densities increases indefinitely as we make the ellipsoid 
sharper and sharper. This leads us to state a principle 
of great importance in the theory of electrical distribution, 
viz., that the electrical density is very great at any pointed 
part of a conductor. 

If we determine the ratio of the densities at two points 
of an ellipsoid,^ diminish the charge, and redetermine the 
same ratio, we shall find that, although the actual densities 
are diminished, the ratio remains the same; and if we 
determine the density at any point of the ellipsoid, and 
then halve its charge by touching it with an equal and 
similar ellipsoid (they must be placed with their axes in 
the same straight line, and made to touch at the poles),' 
and redetermine the density at the same point as before, 
we shall find that the density in the second case is half 
that in the first. We have in fact, in general, the im- 
portant proposition that — 

The density at any point of a conductor is proportional 
to the whole charge on the conductoTy or, what is the same, to 
the mean density. 

The following case given by Coulomb is interesting ; it 
shows the tendency of electricity towards the projecting 
parts, ends, or points of bodies. The conductor was a 
cylinder with hemispherical ends, — the length of the cylin- 
der being 30 inches, its diameter 2 inches. Coulomb 
gives the following results : — 



DiiUnco from ftnd. 


Density. 


h in. 
2 

1 



100 
1-26 
1-80 
2-30 



The density at the end is thus more than twice thac at 
the middle. 

Other results, taken from Coulomb's unpublished papers, 
may be found in Biot,^ Mascart, or Riess. His results for 
a circular disc we shall quote further on. 

^ We sapi»8e in all these experiments that we are dealing with a 
tingle body, sufficiently distant not only from all electrified bcdies but 
from all neutral conductors to be undisturbed by them. This condi- 
tion is essential. 

' It would not do to make the pole of one touch the equator of the 
oUier, or to place them otherwise uusymmetrically. 

* TraiU de Physique 



Ripss made a series of experiments on cubes, cones, kc ; 
but as these are not of theoretical interest, the calculatioD 
in such cases being beyond the powers of analysb at 
present, and as the use of the proof-plane or sphere with 
bodies where edges and points occur is not free from 
objection, we content ourselves with referring to Eiess's 
work for an account of the results. 

Coulomb made a series of experiments on bodies ofck>a- 
different forms, which he built up out of spheres of different lomVt 
sizes, or out of spheres and cylinders. These are of very 'JV. 
great interest, partly on account of the close agreement of ^^^ ^g^. 
some of the results with the deductions subsequently made poaite 
by Poisson from the mathematical theory, and partly on condno^ 
account of the clearness with which they convey to the **"*• 
mind the general principles of electric distribution. His 
method in most cases was to build up the conductor and 
electrify it with all the different parts m contact, and then 
after separating the parts widely, to determine the mean 
density or the whole amount of electricity on each part 
by the proof-plane or otherwise. 

For spheres in contact he found the following results, — 
S, Q, o- ; S', Q', cr denoting the surface, quantity of elec- 
tricity, and mean surface density for the two spheres respec- 
tively. 



5' 


Q' 


V 


S 


Q 





8-86 


8-8 


V09 


14-80 


111 


1-38 


62-00 


37-6 


1-66 



From this it appears that although the whole amount 
of electricity on the large sphere is greater than that on 
the small, yet the mean density for the smaller sphere is 
greater than for the larger. The above result also affords 
an experimental illustration of the action of the earth in 
discharging a conductor connected with it. Comparing 
the conductor to the small sphere and the earth to the 
large sphere of 62 times the superficial area of the small 
one, if we start with charge Q on small sphere and then 
put the two in contact, the charge on the small sphere will 

be reduced to ^^ Q, so that the mean density is dimin- 
ished in the ratio 1 : 38*6. This ratio increases indefinitely 
as the ratio ^ increases. These results are in satisfactory 

agreement with Poisson*s calculations. Coulomb was led 
by his observations to assign 2 as the limit of the ratio of 
the mean densities when the ratio of the diameters of the 
spheres is infinitely great ; the mathematical theory gives 

~ or 1-65. 
o 

Coulomb also determined the density at the apex or 
smaller end of the body formed by two unequal spheres in 
contact The following are his results, the mean density 
of the larger sphere being unity : — 



Ratio of radlL 


Density at apex. 


Obaerred. 


Calculated. 


1 
2 
4 
8 
3 


1-27 
1-65 
2-35 
318 
4 00 


1-32 
1-88 
2-48 
8-09 
4-21 



When two equal spheres are placed in contact the dis- 
tribution will of course be the same in each; Coulomb 
found that, from the point of contact up to a point on the 
surface of either sphere distant from it by about 20*, no 
trace of electricity could be observed ; at 30% 60', W% 



V 



24 



ELECTBIOITY 



[VLBGTSOSTATIOAL THSOXT. 



Defini- 
tions. 



180* respectively, the electric density had the relative 
values *20, *77, *96, 100. When the spheres are unequal 
the distribution is no longer alike on each. On the small 
sphere it is less uniform, and the density at the point of 
the small sphere diametrically opposite the point of con- 
tact is greater than anywhere else on the body. The 
distribution on the larger sphere is more uniform than on 
the smaller, and the more unequal the spheres are the 
more uniform is the distribution on the larger^ and the 
smaller the unelectrified part in the neighbourhood of 
the point of contact. 

The following results of Coulomb are useful illustrations 
of distribution on elongated and pointed bodies : — 

Three eaual spheres (2 in. diameter) in contact, with their 
centres in tne same straight line : the mean densities were 1 '34, 
1*00, 1*34 on the spheres 1, 2, and 3 respectively. 

Six equal spheres as before: mean densities on 1, 2, and 
8- 1*56, 1-05, 100. 

Twelve equal spheres: mean densities on 1, 2, and 6 = 1*70, 
1-14, 1*00. 

Twenty-four equal spheres: mean densities on 1, 2, and 12= 
1*75, 1*07, 1*00. 

Laree (8 in. diameter) sphere with four small (2 in.) spheres 
applied to it, all the centres in line: the mean density on large 
sphere being 1, that on the small one next it was '60 that on the 
extreme small one 2*08. 

Lai^^e sphere 1, and twenty-four (2 to 25) small ones: mean 
densities on 1, 2, 13, 24, 25 = 1*00, -60, 1*28, 1*46, 2'17. 

MATHEMATICAL THEORY OF ELECTRICAL 

EQUILIBRIUM. 

We take as the basis of our theory the assumptions 
already laid down under the head Provisional Theory, and 
in addition the precise elementary law of electrical action 
established by Coulomb. We shall also suppose that we 
have only perfect conductors and perfect non-conductors 
to deal with, the medium being in all cases the same, 
viz., air. When we have to deal with electrified non-con- 
ductors we shall suppose the electrification to be rigid, i,e, 
incapable of disturbance by any electric force we have to 
consider. 

In our mathematical outline we have in view the requirements of 
the physical more than the mathematical student, and shall pass 
oyer many points of great interest and importance to the latter, for 
full treatment of which we must refer him to original sources, such 
as the classical papers of Green, the papers of Sir William Thomson, 
and the works of Gauss. Of peculiar interest mathematically 
is the elegant and powerful memoir of the last — Allgeiaeine Lehr- 
tdtze in Beziehung auf die im verkehrten Ferhdltnisse des Quadrats 
der Ent/emung wirkenden AnziehuTigs- und AbslossungskrdfU, in 
which will be found detailed discussions of tlie continuity of the 
inteffnds used in the potential theory, &c. The works of Green 
and Thomson are too well known in this country to require farther 
remark. 

When, in what follows, we speak of the electric field, we 
mean simply a portion of space which we are considering 
with reference to its electrical properties ; it will be found 
conducive to clearness to regard that space as bounded. In 
general the natural boundary would be the walls of the 
experimenting room ; but, for mathematical purposes, we 
shall, unless the contrary is stated, suppose our field to be 
bounded by a sphere of radius so great that the action at 
a point on its circumference due to an electrified body in 
the field is infinitely small 

The reatdtant force at a point in the electric field is the 
force which would be exerted on a unit of -i- electricity placed 
there without disturbing the electrical distribution else- 
where. It is plain that the resultant force has a definite 
magnitude and direction at every point in the field, and 
consequently is in modern mathematical language a vector, 
A curve drawn in the field such that its tangent at every 
point is in the direction of the resultant force at that point 
b called a line of force. We can draw such a line through 
every point of space, and if we suspend at any point a 



small conducting needle, it is obvious, from what we have 
already laid down about induction, that it will take up a 
position very nearly parallel to the line of force ; so that 
if we start from any point and carry the centre of the 
needle always in the direction in which the needle points 
we should trace out a line of force. 

The poterUial at any point is the work done by a unit 
of + electricity in passing from that point to the infinitely 
distant boundary of the electric field, the electric distri- 
bution being supposed undisturbed. It is usual to call 
the infinitely distant boundary a place of zero potentiaL 
Zero is to be understood in the sense of " point ur posi- 
tion from which we reckon."^ 

Consider two points P, Q, infinitely near each other Fora 
in the field, and draw a curve from P passing through **™ 
Q to 00. Then, if F be the component parallel to^ 
PQ of the resultant force at P, we have by our definition 

or in differential notation 



hence 
and 



ds 



0\ 



Y=/^¥d8=/^(Jidx+Ydy^Zdz) . . . (2), 

where Y denotes the potential at P, and X,Y,Z the components 
parallel to the co-ordinate axes of the resultant electric force. We 
clearly have as particular cases of (I) 

^ dV ^ dV „ dV ... 

^""dS ^=""^ ^="di • • ^^^• 

We may remark that, in all cases which we shall consider at pre- 
sent, the work done in passing fi'om any point to any other point is 
the same whatever the intermediate path of our exploring unit. 
Hence Y as above defined is a single valued function, and m' for- 
mulae (3) gives the components of resultant force when Y is known. 

The work done by a unit of + electricity in passing by 
any path from P to Q is called the electromotive force from 
P to Q; it is obviously equal to the difference of the poten- 
tials at the two points. Thus 

Y^-y^=/^{Xdz+Ydy+Zdz) . . . (4). 

is the electromotive force from P to Q. 

Suppose we concentrate m units of electricity at any point P, and Ezpr 
require the potential due to this at a point Q, distant D from P. don 
Applying (2), and, since any path to oo may be chosen, taking the of Y 
integral along the production of PQ to oo , we get term 

>.oo defin 

Y = / ^rfr=^ .... (5;. ^^ 

If we have any number of discrete points with charges m^^ m^ 

m,,.. .. at distances Dj, D,, D„ from Q, since the work done by 

the exploring unit under the action of the whole is got by adding 
up tlie work done under the action of each part separately, we 
clearly have 

^=cj+S|+*«-^p- • • . ■ («)• 

From this we may pass to the case of a continuous volume distribu- 
tion. If p be the volume density at the point ^i|f, and Y the 
potential at xyz^ we have 



Hff 



pd^drid( 



(7), 



where D denotes + J(^-a;)'+(i|-y)' + (f-z)«, and the integral is 
to be extended over every part of the field where there is any 
charge, — or, which is the same thing, over the whole field, on the 
understanding that o — where there is no charge. 

If, as will generally be the case, the electricity is distributed on a 
surface in such a way that on an element dS of surface there is a 
quantity adS of electricity, where <r is a finite surface density, then 

V~/f ~j^ (8)f 

where D has the same meaning as before, and the integral is ex- 
tended all over the electrified sunace or surfaces. 

* It may be well here to warn the reader that measurement o^ 
potential is relative, just as much as measursment of diiUnoe is, and 
to caaiUm him against the fallacious idea of absolute nro of potentiaL 



■LI0TB06TATI0AL THXOBT.] 



ELECTRICITY 



25 



in- 
tion. 



I0nii- ^0 ^^7 iQAko ^ci^ ^^® important remark that, so long ac p or a 

^ V. if not infinite, the integrals in (7) and (^ are finite and continaous. 

' This depends on the fact, which we cannot stop to prove, that the 

part of tne potential at P, contributeil by an infinitely small portion 

of electricity surrounding P, is infinitely smalL 

In practice, therefore, the electric potential is always 
continuous; for although we may in theory speak of 
discrete points and electriBed lines where finite electri- 
fication is condensed into infinitely small space, yet no 
such cases ever occur in nature. It may also be shown 
for any electrical system of finite extent, that, as the 
distance of P from O, any fixed point at a finite dis- 
tance from the system is increased indefinitely, the 
potential at P approaches more and more nearly the 

M * 

value jT , where M is the algebraical sum of all the 

electricity in the system, and D the distance of P from 0. 
Hence at any point infinitely distant from 0, V = 0. 

We next proceed to prove the following proposition, 
which will form the basis of the subsequent theory : — 
tmf ^^ turf act integral of electric induction taken all over 
ignd the surface inclosing any space is equal to Aw times the alge- 
tlec- braiccU sum of all the electricity in that space. 

By the electric induction across any element of the sur- 
face (taken so small that the resultant force at every point 
of it may be regarded as uniform) is meant the product of 
the area of the element into the component of the result- 
ant force in the direction of the normal to the element 
which is drawn outwards with respect to the inclosed 
space. Thus dS being an element of surface, c the angle 
between the positive direction of the resultant force R and 
the outward normal v, and E the sum of all the electricity 
in the inclosed space, the proposition in symbols is — 

jy'Rcoscc/S=4^E .... (9). 

We shall prove it in the manner most natiutilly suggested by the 
theoTV of electrical elements acting 
at a distance, by first showing that it 
is true for a single element e either 
outside or inside the surface. Let us 
suppose to be at a point P, fig. 11, 
witnin S, which for greater generality 
we may suppose to be a re-entrant 
surface. Draw a small cone of vertical 
solid angle eU» at P, and let it cut the 
surface in the elements QR, Q'R', 
Q^'R"; let the outward normals to 
these be QM, Q'M', ^"14". The ele- 
ments of the surface integral contri- 
buted by QR, QH', Q'Tl" are obviously 

QR^COSf . V . nT> ^«P^' 

QR.=, . ^^^ . and Q'R-^«PH''« 




Fig. 11. 



9laoe 



^^ .. , hence the three elements 
cos • cos f ' 

of the integral become -I- edti, - cdv, + edu ; and the sum is edta. 

Addinfj^ now the contributions from all the little cones which fill up 

tha aohd angle of ir about P, we get 

jJR coB*dS=z^dw = iwe, 

Had the point P been outside, the numbers of emergences and 
entrances would have been equal, the contribution of each cone zero, 
and on the whole 

j7Rcosf<iS = 0. 

Combining these results, we see that the proposition is true for a 
single element. Hence, by summation for all the elements, we can at 
once extend it to anv electrical system ; for all the elements external 
to S give zero, and all the internal elements give 4t2« = 4t£. 

Let us apply the above proposition to the space enclosed by the 
infinitely small parallelepi[)ed whose centre is at xyz, and the 
co-ordinates of whose angles are a;dbi<^ y:kidyfZ:k^s. The con- 
tributions to the surface mtegral from the two faces perpendicular to 



the X-axis are 



-( 



dV 
dx 



dx rf»V 
2 dx* 



).^ana(g-^^)..<i. 



(0^ SI it is Qsoally abbreviated, 



+ 4tp = 0, 



Adding these and the four parts from the remaining sides, and equat- 
ing to ivfdxdydz, which is the 4t£ in this case, we have 

d»V . d«V . d»y 



Equation (10), oiiginally found by Laplace for the casep^O, and 
extended by Poisson, has been called the cnaracteristic equation of the 
potentiaL It may be applied at any point where p is finite and the 
electric force continuous. It mieht oe shown by examining the inte- 
grals representing X, Y,Z,and -=- , &c., that the electric force is con- 
tinuous wherever there is finite volume density. Equation (10) may 
be looked on either as an equation to determine the potential when 
p is nven, or as an equation to determine p whenV is given. We 
shall nave occasion to use it in both ways. 

The characteristic equation cannot be applied in the form Condi- 
(10) when the resultant force is discontinuous. This willtlousat 
be found to be the case at a surface on which electricity is SfiiS^ 
distributed with finite surface density. Let us consider the surface 
values of the resultant force at two points, P and Q, infinitely 
near each other, but on opposite sides of such a surface. 
Hesolve the resultant force tangentially and normally to the 
surface. If we consider the part of the force which arises 
from an infinitely small circular disc, whose radius, though 
infinitely small, is yet infinitely great compared with the 
distance between P and Q, we see that infinitely little is 
contributed to the tangential component at P or Q by this 
disc, while it can be readily shown that the part of the nor- 
mal component arising therefrom is 2^<r, directed /row the 
disc in each case, when a- is the surface density. Hence, 
since the part of the resultant force arising from all the rest 
of the electrified system obviously is not discontinuous be- 
tween P and Q, the tangential component is continuous when 
we pass through an electrified surface, but the nonnal com- 
ponent is suddenly altered by 49rcr. 

For a thorough investigation of these points the reader is referred 
to Gauss or Green. We can arrive very readily at the amount of the 
discontinuity of the normal force by applying (9) to the cylinder 
formed bv carrying an infinitely short generating line round the 
element aS, so that one end of the cylinder is on one side of dS and 
the other on the other, the lateral dimensions being infinitely small, 
but still infinitely ^^reater than the longitudinal. The only part of 
the integral which is of the order of ciS is the part arising from the 
two ends ; hence if N,N' be the value of the normal components on 
the two sides of S, we clearly get 

(N - NO dS - 4T<niS , or N - N'- 4T<r . 

If Vp V, denote the potentials on the two sides of S, and k, , r, the 
normals, to c£S, drawn towards these sides respectively, then we may 
obviously write our equation 

'd^.^d;]^^-^-^ • • • • 



(11). 



(10). 



Written in this form the equation has been called the surface char- Surface 
acteristic enuation of the potential. It may be looked upon as a charac- 
surface condition, which must be fulfilled by the values of V on the teristic 
two sides of an electrified surface on which the surface density <r is equation, 
given, and where, in consequence, there is discontinuity in the first 
oifierential coefficients of V ; or it may be looked on as an equation 
to determine a when V, and Vj are given. 

We have seen that we can draw through every point of Level 
the electric field a line of force. A surface constructed so surface- 
that the potential at every point of it has the same value is 
called an equipotential or level surface. We can obviously 
draw such a surface passing through every point of the field 
It is clear, too, that the line of force at every point must be 
perpendicular to the level surface passing through that point 
For since no work is done on a unit of + electricity in 
passing from one point of a level surface to a neighbouring 
point, there can be no component of the resultant force tan- 
gential to the surface; in other words, the direction of the 
resultant force is perpendicular to the surface. This is ex- 
pressed otherwise by saying that the lines of force are 
orthogonal tra^^ries to the level surface. 

If we take ^|Piall portion of a level surface, and draw Tubes 
through eveiy pomt of the boundary a line of force, we shall force, 
thus generate a tubular surface which will cut orthogonally 
every level surface which it meets. Such a surface is called 
a tube of force. 

Let a tube of force cut two level surfaces in the elements 
(jS and cfS'. Apply to the space contained by the part of the 

VIIL — 4 



26 



ELECTRICITY 



[electrostatigal TRSOST* 



Import- 
aut pro- 
perty of 
tabes of 
force 



Charge 
mea- 
anred by 
tubes of 
force. 



tube between the surfaces our fundamental eqaation (9). 
We thus get, since there is no normal component perpen- 
dicular to the generating lines of the tube, 

K(iS-R'c/S' = 0, .... (12), 

provided the tube does not cut through electrified matter 
between the two surfaces. Here K and R' denote the resul- 
tant force at dS and d'Sj which are supposed so small that the 
force may be considered uniform all over each of them. It 
appears then that the product of the resultant force into the 
area of the normal section of a tube of force is constant for 
the same tube so long as it does not cut through electrijied 
matter ; or what amounts to the same, the resultant force at 
any point of a tube of force varies inversely as tlie normal 
section of the tvhe at tliat point. 

If we divide up any level surface into a series of small 
elements, such that the product 11^3 is constant for each 
element and equal to unity, and draw tubes of force through 
each small element, then the electric induction through 
any finite area of the surface is equal to the number of tubes 
of force which pass through that area; for if n be that 
number, we have, summing over the whole of the area — 

2R<iS = n (13), 

the left hand side of which is the electric induction through 
the finite area. It is clear, from the constancy of the pro- 
duct BdS for each tube of force, that if this is true for one 
level surface it will be true for every other cut by the tubes 
of force. It is evident that the proposition is true for any 
surface, whether a level surface or not, as may be seen by 
projecting the area considered by lines of force on a level 
surface, and applying to the cylinder thus formed the surface 
integral of electric induction, it being remarked as obvious 
that the same number of tubes of force pass through the 
area as through the projection. This enables us to state 
the proposition involved in equation (9) in the following 
manner : — 

The excess of the number of tubes of forces whichleave a 
closed surface over the nurabei' which enter is equal to 4ir times 
the algebraical sum of all the electricity vnthin the surface, 

(N,B. — The positive direction of a line of force is that 
direction in which a unit of -f electricity would tend to move 
along it.) This proposition enables us to measure the charge 
of a body by means of the lines ^ of force. We have only to 
draw a surface inclosing the body, and very near to it, and 
count the lines of force entering and leaving the surface. 
If the number of the latter, diminished by the number of 
the former, be divided by 4ir, the result is the charge on the 
body. 

If we apply (13) to a portion of an equipotential surface 
so small that H may be considered uniform over the whole 
of it, we may wrifce 






(14); 



force. 



Besult- or in words : — The resultant force at any point is equal to 
ant force i\^ number of lines of force per unit of area of level surface 
JJI^^ at that point, meaning thereby the number of lines of 
lines of force which would pass through a unit of area of level sur- 
face if the force were uniform throughout, and equal to its 
value at the point considered. 

We are now able to express by means of the lines of 
force the resultant force at any point of the field, and the 
charge in any element of space. The electrical language 
thus constructed was invented by Faraday, who continually 
used it in his electrical researches. In the hands of Sir 
William Thomson, and particularly of Professor Clerk Max- 
well, this language has become capable of representing, not 

^ Here we' drop the distinction between line and tabe of force. We 
shall hereafter suppose the lines of force to be always drawn so as to 
form unit tubes, and shall speak of these tubes as lines of force, thereby 
following the nsoal custom. 



only qualitatively but also quantitatively, with mathematical 
accuracy, the state of the electric field. It has the additional 
advantages of being well fitted for the use of the practical 
electrician, and of lending itself very readily to graphical 
representation. 

It will be convenient, before passing to electrical applica- 
tions, to state here another general property of the potential 
which follows from our fundamental proposition. 

The potential cannot have a maximum or minimum value 

at a point where there is no electricity. 

For if a maximum value were possible, we could draw round the 
point a surface at every point of which the potential was decreasing 
outwards ; consequently at every point of this surface the normu 
component of the resultant force in the outward direction would be 
positive, and a positive number of lines of force would leave the 
surface. But this is im]>ossible, since, by our hypothesis, there is no 
electricitgr within. Similarly there could be no minimum value. 

From this it follows at once that if the potential have ike 
same value at every point of the boundary of a space in which 
there is no electrified body, then the potential is eongtant 
throughout that space, and equal to the value at the boundary. 
For {f the potential at any point within had any value 
greater or less than the value at the boundary, tlus would 
be a case of maximum or minimum potential at a point in 
free space, which we have seen to be impossible. 

In order that there may be electrical equilibrium in a 
perfect conductor, it is necessary that the resultant electric 
force should be zero at every point of its substance. For if 
it were not so at any point the positive electricity there 
would move in the direction of the resultant force and the 
negative electricity in the opposite direction, which is incon- 
sistent with our supposition of equilibrium. This condition 
must be satisfied at any point of the conductor, however near 
the surface. At the surface there must be no tangential 
component of resultant force, otherwise electricity would 
move along the surface. In other words, the resultant force 
at the surface must be normal ; its magnitude is not other- 
wise restricted -^ for by our hypothesis electricity cannot 
penetrate into the non-conducting medium. 

These conditions are clearly sufficient. We may sum 
them up in the following single statement : — 

If the electricity in any conductor is in equilibrium, the 
potential must have tlie same value at every point in its 
substance. 

For if the potential be constant, its differential coefficients 
are zero, so that inside the conductor the resultant force 
vanishes. Also the surface of the conductor is a level sur- 
face, and therefore the resultant force is everywhere normal 
to it This constant value of the potential we shall hence- 
forth speak of as the potential of the conductor. 

Since the potential is constant at every point in the 
substance of a charged conductor, we have at every point 
V2V = 0, and hence by the equation of Poisson p = 0; that 
is, there is no electricity in the substance of the conductor. 
We thus get, as a theoretical conclusion from our hypothesis, 
the result already suggested by experiment, that electricity 
resides wholly on the surface of conductors. 

If we apply the surface characteristic equation to any 
point of the surface of a conductor, we get 

which gives the surface density in terms of the resultant 
force and reciprocally. 

We may put this into the language of the lines of force 
by sajring that the charge on any portion of the surface of a 
conductor is equal to the number of lines of force issuing from 
it divided by 4ir. 

Since the surface of a conductor in electric equilibrium 

' Of course in practice there is an upper limit, at which diuuptlvD 
discharge occurs. 



Man- 
mam* 
minin 
poieol 
impoi 
sible 
infrn 
space. 



Case« 

space 
boaik 
by Isi 
saHu 



Condi 
tion c 
electr 
eqnfli 
brian 



Elee- 
tridtj 
reside 
on th 
mxxfat 



c = 



XL10TB08TATICAL THXORT.l 



ELECTRICITY 



27 



mt in 
Uow 
ndoc- 
r. 



idirect 

idence 

rthe 

w of 

▼ene 

iiure. 



t>blem 

icml 
ftribu- 

BO* 



is always a level surface, it follows, from what we have 
already proved aboat a space boauded by a surface of con- 
stant potential, that, inside a hollow conditctor the potential 
is cansianty provided there he no electrified bodies vrithiiL 
This is true, no matter how we electrify the conductor or 
what electrified bodies there may be outside. Hence, if 
we inclose any conductor A completely within another B, 
then electrify B and put A in metallic communication with 
it, A will not become charged either + or - ; for, A being 
at the same potential as B, electricity will not tend to flow 
from the one to the other. This is in reality Biot's^ ex- 
periment with the hemispheres, to which we have already 
alluded ; only the point of view is slightly changed. The 
most striking experiment ever made in illustration of the 
present principle is that described by Faraday in hio 
Experimental Researches, He constructed a hollow cube 
(12 feet in the edge) of conducting matter, and insulated 
it iu the lecture-room of the Royal Institution. We quote 
in his own words the part of his description which bears 
on the present question : — 

**1172. I put a deh'cate ^Id-leat alectrometer within the cube, and 
then charged the whole by an outside communication, very strongly 
for some time' together ; but neither during the charge or after the 
dischai;pe did the electrometer or air within show the least sign of 
electricity. .... I went into the cube and lived in it, and using 
all other tests of electrical states, I could not find the least influ- 
ence npon them, though all the time the outside of the cube was 
powerfully chaiged, and large sparks and brushes were darting olx 
from every point of its outer surface." 

The proposition that the potential is constant inside a 
hollow conductor containing no electrified bodies may be 
regarded as one of the most firmly established in the 
whole of experimental science. The experiments on which 
it rests are of extreme delicacy. It . is of the greatest 
theoretical importance; for we can deduce from it the 
law of the inverse square. Taking the particular case of 
a spherical shell, uninfluenced by other bodies, on which 
of course the electrical distribution must from symmetry 
be uniform, it can be demonstrated mathematically that, 
if we assume the action between two elements of electricity 
to be a function of the distance between them, then that 
function must be the inverse square, in order that the 
potential may be constant throughout the interior. A 
demonstration of this proposition was given by Caven- 
dish, who saw its importance ; a more elaborate proof 
was afterwards given by Laplace ; for a very elegant and 
simple demonstration we refer the mathematical reader 
to Clerk Maxwell's Electricity, vol. i. § 74. This must be 
regarded as by far the most satisfactory evidence for the 
law of the inverse square ; for the delicacy of the tests 
involved infinitely surpasses that of the measurements 
made with the torsion balance; and now that we have 
instruments of greatly increased sensitiveness, like Thom- 
son's quadrant electrometer, the experimental evidence 
might be still further strengthened. 

In the problem to determine the distribution of elec- 
tricity in a given system of conductors, the data are in 
most cases either the charge or the potential for each con- 
ductor. If the conductor is insulated it can neither give 
nor lose electricity, its charge is therefore given. If, on 
the other hand, it be connected with some inexhaustible 
source of electricity at a constant potential, its potential 
is given. Such a source the earth is assumed to be ; and 
we shall henceforth take the potential of the earth as 
zero, and reckon the potential of all other bodies with 
reference to iL If all our electrical experiments were con- 

^ The experiment was first made by Cavendish. There is an account 
of it in hii hitherto unpublished papers. 

' Fknday was looking for what he called the absolute charge of 
matttr ; Incidentally the experiment illustrates the point we are dis- 
ooMin^ 



ducted in a sjmce inclosed by a perfectly conducting enve- 
lope, the potential of this envelope would be the natural 
zero of our reckoning. 

It will be useful to analyse more closely the distribution 
on a system of conductors, in order to see how far the 
above data really determine the solution of the electrical 
problem. For this purpose the following proposition is 
useful. If Cj, f 2> • • • • ^n be the charges at the points Principle 
1, 2, .... n of any system, and V the potential at P, o^«loo- 
and if V be the potential at P due to e^, e^y . . . . tf„' at J^™^. 
1, 2, . . . . », then the potential at P due to ^i + ^i'i sition. 
<?2 4- e^y .... at 1, 2, .... is V + v. This principle fol- 
lows at once from the definition of the potential as a sum 
formed by the mere addition of parts due to all the single 
elements of the system. 

Applied to a system of conductors in equilibrium, it 
may evidently be stated thus: If E^ Eg, .... E« and 
Vj, Vj, .... V„ be the respective charges and potentials 
for the conductors 1, 2, 3 .... ri in a state of equilibrium, 
Ej', Ejj', . . . . E„' and V/, Vg', . . . . V/ corresponding 
charges and potentials for another state of equilibrium, 

then Ei + E/ E. + E„', V^ + V/ V, -4- V/ will be 

corresponding charges and potentials for a third state of 
equilibrium. 

Suppose that in the system of conductors 1 , 2, 8, n the con* Particu- 

ductor 1 is kept at potential 1 and all the others at potential zero, Ur case 
then it can be shown that there is one and only one distribution of of general 
electricity fulfilling these conditions. Mathematically stated, the problem, 
problem is to determine a function Y, which shall satisfy the equa- 
tion v*V=0 throughout the space unoccupied by conductors, and 

have the values 1, 0, 0, was respectively at each point of the 

surfaces of 1, 2, n respectively. 

Consider the integral 

where the integration is extended all over the space unoccupied by 
conductors. If we consider all the values which this integral may 

have, consistent with the boundary conditions V-1, V-0, 

&c. at the siu-faces of 1, 2, &c., it is obvious that there must 

be a minimum value ; for the integral is essentially positive, and 
c^mnot become less than zero. 



Now 81-2^^(2 '^£^+^"- y^^y^ 

^2 fffh\v^\dxdydz .... 



07) 



by partial integration. The surface terms vanish, since 5V-0 at 
every surface. Hence v^V-O is the condition for a maximum or 
minimum value of I, and since we know that a minimum value 
exists, there must be a solution of this equation. It can, moreover, 
be shown, by a method which we shall apply below to the more 
general problem, that there is only one solution of v*V = con- 
sistent with the given conditions, and this will of course be 
that which makes 1 a minimum. If our mathematical methoda 
were powerful enouj?h to determine V, we might proceed to 
find the surface density for each conductor by means of the formula 

<r - - 7- : then the charges on the conductors could be found 

i-w aw " 

by means of the integral - i^jf-J-J^ • ^° ^^^ ^^^ ^^^^^ 

indeed could we actually find these cnarges ; we have, however, de- 
monstrated their existence and shown that our problem is definite. 

Let these charges on 1, 2, ... n be called 7i i» 9i 2 • • • 5i ••• Coeffi. 
Corresponding to the data 0, 1, 0, .... for the potentials dents of 

of 1, 2, ... w, we should get a series of charges 92 p ^a 2» capacity 

q^ „, and so on ; 9i x, (?2 2. ^3 3 • • • ^^e called the coefficients of J^^ 
self-induction or capacity for the conductors 1, 2, o, . . . ; 
?i 2» ^1 s» ^^"» *^® ^^^^^ ^^ coefficients of induction of 1 on 
2, 1 on 3, <fec. It is obvious that these coefficients depend 
solely on the form and relative position of the conductors. 
It follows, from the principle of the superposition, that, if 
1, 2, ... n be at the potentials V,, 0, ... 0, then the 
charges on them will be n-^ ,Vi, q^ 2 m • • • • ^^ ^ ^* 



28 



ELECTRICITY 



[klect&ostatigal thsost. 



may construct then a series of states of equilibrium repre 
sented thus : — 

Potential, J V^ \ | | | 



Potential, I | V i | | . .. I 

Chaige I S'liV, | gj,V, | g^jV, | | q^n^t 

and so on. Superposing all these, we get a system in 
equilibrium, in which the potentials are Y^, Vj, . . . Y^, and 
the charges 

Bi =?iiVi + !7,iV,+ . . . +qnjn ) 

Ej -?iiVi+y,,V,+ . . . + y,,Vn > . . . (18). 

&c. — &c ) 

It appears therefore that the 2n quantities E^, <fec, Y^, &c., 
are connected by n linear equations ; so that when n of 
them are given, the rest can be determined in terms of 
these in a definite manner. 

Returning then to our general problem, we see that, 
when either the charge or the potential is given for each 
conductor, the electrical problem is determinate, and a 
solution is given by the linear equations of (18). The 
potential at any point of the field can be written down 
very easily. Suppose in fact v^ to be the value at the 
point P of the function Y which we determined in solving 
the case where the potentials 1, 0, 0, .... are given for 
1, 2, ... n, ^2 the corresponding function for the case 
0, 1, 0, ... 0, and so on. Then the potential at P in the 
general case is obviously 

V«YiVi + Y2t;2 + +Y„v^ . . (19), 

where v^, Vj, ... t;„ are all known functions, and 
Yi, Yg, . . . V^ are all either given, or determined in terms 
of given quantities by the equations (18). 

It is very easy to show that there is no other solution 
of th& problem than the one we have found. 

Suppose in fact that V is a function different from V, which 
satisnes nil the conditions of the problem. Consider the function 
U = V- V, since V and V both satisfy the equation v'V=0, we 
have v*U = 0. Also at surfaces where V is given U— 0. At 
surfaces where V is not given, we have U= constant -constant — 
constant ; and, since in this case the charge wil' be given, we shall 
have 

/fT,^=ff%^' andtheKfore//"^rfS-0. 



Now we have 



rff\k 

//A 



E -£■)'*'* I"''' 



ril 



rfU. dU' dU. I oxdydz 

dx\ dy\ dz\ \ 

The first term vanishes for all the surfaces, — for some because U — 

for others because U is constant and / / ~j~dS=.0; and the second 

term vanishes because v'U — 0. 

Hence the integral on the left hand must vanish, and that too 
element by element, since every element is positive. Hence we 
must have 

dV dV' dV dY' dV dV' 
dx "dx ' dy " dt/ ' dz " "dz ' 

Hence V and V can only differ by a constant But such differ- 
ence is precluded by the boundary conditions. Hence the func- 
tions are identical ; in other words, there is but one solution to the 
problem we have proposed. 

It is very easy to show, by methods of which we have 
already had an example, that the value of Y thus found 
makes the integral 

a minimum. Now, we shall show directly that this inte- 



gral represents the potential energy of the system, ft 
follows, therefore, that the distribution which we hava 
found is in stable equilibrium. 

If we solve the equations (18), we shall get 



. . . . 



Pn 



E, 



Yi=i?ii Ej+i?,, E,+ . . . . Pn, E*!. 
&c. 



(20), 



A set of equations which we might obviously have Coifll. 
arrived at by first principles. The physical meaning of the ^^ 
coefficients Pi^Pi^ and Pm ^ very obvious; they are 5***" 
the potentials, corresponding to a state of equilibrium, in 

which the charges on 1, 2, 3, n are 1, 0, 0, . . . 0, and 

80 on. Pi 1, l?i 2> • • ^^i ^^^ called coefficients of potential; 
and, mutatis mutandis, all the remarks already made about 
^i V ?i 2' ^c-j ^PP^y *^ ^^®°^ Many interesting and im- 
portant theorems have been proved about these coeflacienta, 
for which we refer the reader to Maxwell {Electricity, voL 
i. chap. 2), whose treatment of the subject we have in the 
main been, folio wing. One of these, of great importance, 
we shall prove here, because it leads us to state a very 
important general theorem, which we shall have occasion 
to use again. 

The mutual potential energy of two electrical 83r8tem8y lleor 
A and B, is the work done in removing the two systems o^^^^ 
to an infinite distance from each other, the internal arrange- JJJJ^ 
inent of each system being supposed unaltered during the 
process. It is clear that we may suppose either that A is 
fixed and B moves off to infinity, or that B is fixed and A 
moves ; the*work done in both cases is, by Newton's third 
law of motion, the same. This is sometimes expressed by 
saying that the potential of A on B is the same as that of 
B on A, 

In fact, the expression for the mutual potential energy is 

(21), 



encfg; 






where q is any element of electricity belonging to A, and ^ any 
element belondng to B, and D is the distance between tliem, the 
summation being extended so as to include every pair of elements. 
We may arrange (21) as follows : — 

each group belonging to a point in B, or, as we may write it, 

?i'^i+?s' Vi+&c., or %qY. 
We may also arrange (21) in the form 

(7i2|^+S',2,^ + &c., 

each group belonging to a point in A. Hence we have the follow* 
ing eq^uahties : — 



2gT=2^=2gV' 



(22). 



The first and last of these expressions are called respectively the 
potential of A on B, and the potential of B on A, and this equality 
explains the statement made above. 

The two systems A and B may be different states of equi- 
librium of the same system, if we choose. In this case we 
may still farther modify the expression in (22), and write 

V j2j5'' + V^jj^ + &c. = V/Jjg + V,'2j/z + &c. (See Gauss, I c) 

So that we may state the proposition thus : — If E^, £3, 
. . . E„, Vj, Vg, . . . V« , and E/, Eg', . . . E^, V/, Vj , . . . V, 
be the respective charges aud potentiak^ of the conductors 
in two different states of equilibrium, then we have 

2E'V = 5EV' .... (23). 

If we take for the two states of the system 



and ±^ 



V 
V 



2ll 
1 





ill 


1-^ 





Jit 




q\n 


2L2. 




equation (23) becomes 



&i-2^i« 



(24). 



BLIOrROCTATUUL TBBOST.] 

or, ia words, tha coeffieimt of tndvetum of \ on 2 it equal to 
that of 2 on \. 
>l There is one more gener&l theorem on electrical distribu- 
tioa which, from its great practical importaace, deserves a 
' place here. Suppose we bxbe a hollow conductor of any 
form, place any electrical system inside it, and connect the 
conductor with the earth, then equilibrium will be estab- 
lished, in such a way that the potential of every portion 
of the conductor ia lero. Now, the potential being zero 
kt all inGnitely distant pointa, we may regard the outside 
apace as inclosed by a surface of zero potential ; hence the 
potential at every point in this space must be the same, 
and there can be no electrical action anywhere ontside. 

Again, removing the internal system, let us place any 
system ontside the conductor, and, besides, charge it to 
any desired extent, keeping it insulated this time. Then 
the outer and inner snrfaces of the conductor will be level 
Burfocea ; and, since there is no electricity inside the inner 
surface, the potential in the interior will be constant. 
Hence the ex temaL system, in a state of equilibrium, exerts 
no action whatever within. Now we may evidently, with- 
out mutual disturbance, superpose such an internal and 
external system as we have described, and still get a 
system in equilibrium. It is, moreover, clear that we can 
in this way satisfy the most general conditions that can be 
assigned. Hence, since we know that there can be only 
one solution of the problem of electrical equilibrium, the 
synthetical one thus obtained represents the actual state of 
aiSeirs. When, therefore, a hollow conductor with any 
external and internal systems is in equilibrium, the equili- 
hrium of the internal U independent of that of the external 
tyaem. 

Moreover, if we draw any surface in the tiibttanee of the 
hollow conductor, no hues of force cross it in one direction 
or the other; therefore the whole amount of electricity 
within must be zero ; in other words, the charge on the in- 
ternal wurface of the eonductor i» equal and opposile to the 
algfbraical turn of the charget on ail the bodie* within. 

These propositions contain the principle of what are 
called electrical screens, i.e. aheeta of metal used to defend 
' electrical instruments, &c., from external influences. On 
the practical efficiency of gratings in this way, see Slaxwell 
(S 203) i on the application to the theory of lightning 
conductors, see a paper by him in the reports of the British 
Association for 1876. 

If we take the simple case where there is no external 

system, but only a charge on the hollow conductor, we get 

a complete explanation of Faraday's ice-pail experiment 

tl The potential energy of a system of charged conductors 

°' is the work required to bring them from a neutral state to 

° the charges and potentials which they have at any time. 

The state of zero potential energy here contemplated is of 

course that in which there is an equal amount of + and 

— electricity everywhere in the system, or, as we might 

put it, the state in which there is no electrical separation. 

Now if Q denote the potential energy of the system, we 

have vrith the notation of (21) 

Q-s^ (26). 

the summation including every pair of elements in the 
system. If the system be in equilibrium, then, reasoning 
as above, it is obvious that 2EV is just twice 2^, inas- 

nndi OS each pair of elements will come in twice. Hence 
we get 

Q-iaEv (28). 



ELECTRICITY 



. i a a 3„v,v,= i 3 3p„!;e. . 



29 



So that Q is a homogeneous quadratic function of tin 
potentials or of the charges. If, therefore, we increase the 
potentials of all the conductors, or the charges of all the 
conductors in any ratio, we increase thereby the potential 
energy in the duplicate of that ratio. 

We can by a transformation, which is a particular case 
of a theorem of Qreen's, obtain a veiy remarkable volume 
integral for the potential energy of an electrical system. 

Let V denote the potential st any point in the field. Consider Qreen's 
the integral tbMtau. 

where the intef^Uon is to be eitcnded thronghont the whole of the 
space unoccupied by condoclots. We have by partial intention 

and tro similar equstioDi. Hence 

where the lorface integration extends over the mirface of all the 
conductors, aud it is to beuiticed thate{i> is dtaim/nnTt Mteon- 
iviOar into the insulating mediam. If f and a be volume and 
surface densities, 

1 dV 
'■"*» d»' 
Thus we |^t 



_ 3r. andfl-- 



This is an expression of the greatest importance. We can 
give it Tarioos forms; by means of (18) and (20) we get 



This result includes a more general case than our present 
one ; for it shows that the potential energy of an electrical 
system is given by the integral on the left hand side in all 
cases, whether there is equilibrium or not. It is not even 
restricted to the cose oE perfect condnctors and perfect non- 
conductors, for a slight modification of our preliminary 
statements would include that case as well. At present, 
however, we have p = everywhere, and V constant at the 
surface and in the substance of each conductor, so that the 
right hand side is simply the expression J2EV which we 
have already found for the potential energy ; we may tbero- 
fore write 

'hffj ™ <»)• 

R being the resultant force at any point of the field, and dv 
the element of volume. It ia clear that we may if we like 
extend the integration over the xehoie field, since in the 
substance of any conductor R^O. 

When we know the potential energy of an electrical sy»- jajtit 
tern it is very easy to find the force which resists or tends to tvullng 
produce any change of configuration. Two particular cases ^ pro- 
are of common occurrence and of considereble interest g^JUJ 
First, let the chai^fes on all the conductors be kept eon- oonflgn- 
stant Let the variable which is altered by the supposed ntion. 
change of configuration be ^ and let 4> be the correspond 
ing force' tending to increase ^ Then, since no energy 
is supplied from without, if we suppose the displacement 
made infinitely slowly, so that no kinetic energy is geD» 
rated, we have 

unoaot tH work per 



$0 



ELECTRICITY 



[elbot&ostatigal thsobt. 



or 



♦«^ + 8Q = ; (30). 

— g >'"■ 

Referring to the second of the expressions in (27), we see that this 
may be written 



♦ =-42 2 ErE.- 



r»l «-rl 



dip 



From this it is evident that in similarly electrified states 
of the same system the force tending to produce a given 
displacement varies as the square of the electrification. 
It is important to remark that in the present case the sys- 
tem tends to move so that its potential energy is decreased. 
Secondly, let us suppose that the potentials of the dif- 
ferent conductors are kept constant during any displace- 
ment, energy being supplied from without. 

We shall suppose the change made in two steps. First, we shall 
suppose the given displacement to take place while the charges 
remain constant. On this supposition the force exerted will, to the 
first order of small quantities, be the same as that exerted when 
we suppose the potential not to vary ; hence 

Next, supply energy from without so that the potentials become 
again Vj, V,,&c., . . . and the charges Ej + JEj , K + JE,, &c. The 
final result will be the same, to first order of small quantities, as if 
the two changes had been made simultaneously. Now, applying the 
theorem of mutual potential energy to the two states of our system, 



E 

T 



El 



E, 



and -y 



2(Ei + «Ei)(Vi+«Vi)^2(EV), 
2E«V=-2V«E . . 



E J + 8 E| ■ Eg + SEj 



we have 
hence 

dV dE dO 

therefore ♦= -l2E^^- = i2V ^= ^(V const.) 



(32); 
(33). 



If ^Qrt 



By (27) this may be written 

♦ = i as v,v.^ 

The energy supplied from without is 

i{2(E + aE)V-SE(V + «V)} 

=i5«EV-iJE8V- -2E«V=2*«^=2«Q, by (82). 

In other words, when the potentials of a system are 
kept constant by supply of energy from without, the system 
tends to move so as to increase the potential energy of 
electrical separation, and the amount of energy supplied 
from without is double this increase. If we suspend side 
by side two balls, each connected with the positive pole of 
a battery, the other pole of which is connected with the 
ground, the balls will tend to separate, and in separating 
they will gain with reference to gravity a certain amount hQ 
of potential energy ; the charges on the balls will also in- 
crease to an extent representing an increase of electrical 
potential energy 8Q, and the batteries will be drawn upon 
for an amount of 28Q. 
Cases The problem of electrical equilibrium has been com- 

where pletely solved in very few cases. We proceed to give a 
P'^^J®™ short sketch of what has been done in this way, which may 
solved. ° ii^dicate to the reader what is known on this head. 
ElliDfloid ^® ^^^ deduce. the distribution and potential in the case 
' of an ellipsoid from known propositions about the attrac- 
tions of ellipsoidal shells of gravitating matter. 

Consider an ellipsoidal shell, the axes of whose bounding sur« 

J— jr J- 

£ace8are(a,ft, c)(a+(ia,ft+d6, c+(ic), where —- — - — -u. .The 

a c '^ 

potential of such a shell at any internal point is constant, and the 
equipotential surfaces for external space are ellipsoids confocal with 
(a, 6, c). (See Thomson and Tait, §§ 519 sqq.) Hence if we dis- 
tribute electricity on an ellipsoid (a, 6, c) such that its density at every 
^int is proportional to tne thickness of the shell formed by the 
similar ellipsoids (a,6,c)(a + (to,& + d6,c + dc), the distribution will be 
in equilibrium. Thus if <r— Atfp, where e is the thickness at any 
point and p the volume density of the shell ; then the quantity of 
electricity on any element c£S is A times the mass of the correspond- 
injy^ element of the shell; and if Q be the whole quantity of elec- 
tricity on the ellipsoid, Q— A times the whole mass ni the shelL 



The mass of the shell is \irpd(dbc) — i-wfjuohep^ therefore Q * kiw^iaJbc^ 
Also B^tip where p is the perpendicular from the centre of the 
ellipsoid on the tangent plane. Wlicnce we get 

,_^ 

iirahc 



(84); 



that is, the density at any point varies directly as the 
distance of the tangent plane at that point from the centre. 

Returning again to our ellipsoidal shell, we know that the result- 
ant force at any external point P due to this shell is to that due 
to a ''confocal shell" passing through the point in the ratio 
of the masses. Let the volume density in the two be p, and let 
the perpen dicula r on the tangent plane at P to the confocal 

(Vos + A, V^+x, V<^ + A.) through P be w. Then the thickness of 
the shell at P is /m^, and the force at P due to the shell iwpftm. 
Hence the force due to the original shell is 






(a). 



dy being an element of the normal at P. Now if a;,y,s be the co- 
ordinates of P, we have, by differentiation of 



«• ^_^ 



f 



a« + A. 6« + A c« + A 



-1, 



2xdx 2ydy 2zdz ( g» y» g* ) ^, 

a« + A"*'6« + A c^ + a" ((a' + A)«"*'(6a + A)«"*'('?TA? J 
Suppose we take dx, dy, dz in the direction of the normal, then 

dx'-'dy _, . > I &c., and the last equation reduces to 



a' + A 

Hence from (a) we get 

^dV" 



dK'^2wdp, 

2wpuabed\ 

V(a« + A)(6« + A)('?TA) * 



Integrating this from A to 00 , and remembering that the potential 
vanishes at an infinite distance, we get 



Y—2wouabc 



/CO 



dK 



V(ai-»-A)(62 + A}(c« + A) 



()B). 



We pass from this to the electrical case by putting for iirp/Aobc, 
whicn is the mass of the shell, Q, which represents the quantity of 
electricity on the ellipsoid. We thus get 

V-g-/" "^ . . . (35).>" 

which gives the potential due to a charge Q on an isolated 
ellipsoid abc at any point on the confocal ( »Ja^ + Ai >/6*-fA, 
Jc^ -f A) . It is obvious that, of the three confocals at P, 
that is meant which belongs to the same family as (a, 6, c), 
e.^., if (a,6,c) be an ellipsoid, as opposed to a hyperboloid of 
one or two sheets, then ( Ja^ + A > njb'^ ■{- A > J<^ -{■ A) must 
be an ellipsoid. 

If we put A = 0, we get the value of the potential V^ at 

Q . 
the sur^ce. Now rp is what we have defined above as 

the capacity of the ellipsoid; we get therefore in the recipro- 
cal of the integral 

d\ 



27C 



(86), 



V(a« + A)(62 + A)(c« + A) 

an expression for the capacity of an isolated ellipsoid. 

In the particular case of an ellipsoid of revolution, the Plane- 
above integral, which is in general an elliptic integral, ^ 
can be found in finite terms. In the case of a planetary **^P" 
ellipsoid, a'=b>c; and we find for the capacity 






• (87). 



where c is the least angle whose tangent is / ^ . 

If we make c = 0, then c = ; and the planetary ellipsoid Circnl 
reduces to a circular disc, the capacity for which is Uiere- ^^ 

2a 1 

fore — , that is, ; - ^, that of a sphere of the same radius 
tt' ' 1-571 ^ 

^ This demonstration was suggested hy that given by Thomson 
[BeprirU 0/ Papers, p. 10) to establish a slightly different formula. 



SLBOIBOSTATIOAL THSOBY.] 



ELECTRICITY 



SI 



(for the capacity of a sphere is obviously equal to its 
radius). Cavendish had arrived by ezperimeut at the 

value t:^ (see Thomson's Reprint, p. 1 80), a very remark- 
able result for his time. It is very easy, by taking the 
limit of the right hand side of (34), to find the expression 
for the density at a distanee r from the centre of the disc ; 
it is 

aj In the case of an ovary ellipsoid, a = 6<c; and the 
^^ capacity is 

log^'!±^S^ .... (89); 



\c -Vc^ 



m 



from which several limiting cases may be deduced. 

Formula (34), applied to a very elongated ovary ellip- 
soid, shows us that the density at the pointed ends is very 
great compared with that at the equator. The ratio of 
the densities in fact increases indefinitely with the ratio of 
the longest to the shortest dimension. We have in such 
an infinitely elongated ellipsoid an excellent type of a 
pointed conductor. 

The efiect of a point or an edge on a conductor may be 
very easily shown by drawing a series of level surfaces, the 
first of which is the surface of the conductor itself, which 
has, say, an edge on it. The consecutive surfaces have 
sharpness of curvature corresponding to the edge, which 
gets less and less as we recede from the conductor. The 
level surfaces at an infinite distance are spheres. Tracing, 
then, any tube of force from an infinite distance, where 
the sections of all are equal, inwards towards the discon- 
tinuity, we see that the section becomes narrower as the 
curvature of the level surfaces sharpens, and at a mathe- 
matical edge the section is infinitely small, and therefore 
the force is infinitely great. At a mathematical point this 
is doubly true. At such places the force tending to drive 
the electricity into the insulating medium becomes infinite. 
In practice the medium gives way, and disruptive discharge 
of some kind occurs. 

We can find the distribution on a spherical conductor in- 
fluenced by given forces, such for instance as would arise 
from rigidly electrified bodies in the neighbourhood. 

The method of procedure would be as follows : — Let U be the 
potential of the rigidly electrified system alone at any point of the 
sphere. Then the problem is to determine a function V, which 
anall satisfy the equation v'V at every point of space, and have the 
value C - U at the surface of the sphere, where C is a constant to 
be determined bv the conditions of tlie problem. Expand C - U in 
aeries of surface harmonics, and let the result bo 



Then the value of Y is 



&c. 



"■■'yo+ 71 " + ')'«-+ . . . inside the sphere 



and r-7 «+y.«f +yA\ 



outside 



(a). 
(7). 



For theM evidently satisfy Laplace's equation, have the given value 
(«) at the suHace of the sphere, and arc finite and continuous 
everywhere. From {$) and (7), by means of the surface characteristic 
eanation, we can deduce an expression for the density at any point 
01 the sphere, and for the whole charge. If the latter is given we 
have a condition to determine C; if, on the other hand, the 
value of the potential of the s^^hero were given, then this would be 
the value of C. 

I of The case of two mutually influencing spheres was treated 

by Poiason in the famous memoir which re&lly began the 

,oii*g mathematical theory of electricity. We regret that we 

jsls. cannot afford space for more than a mere sketch of his 

methods. 

Consider the potentials due to the distributions on each sphere. 
Let a and h be toe radii of the two spheres, r and / the distances 



of any point P from their respective centres, and fi and a' the cosines 
of the angles r and / make with the line joining the centres of 
the spheres. Since the distributions are evidently symmetrical 
about the central line, we can obvioudy expand the potentials 
due to each distribution in zonal harmonics relative to the cor- 
responding sphere. Hence, if 4ira^ ( M» - ) denote potential due to 
sphere a at any point inside it, we have 

The potential at any external point is 

Ao7+AA^' + A,Q,fj'.| . 
which may be written 4ir — ^[ /i, - j . 
Similarly we have fot the other sphere 

4irfc*U', t1 -Bn + B^Q/^ + B.O'.d' + . ... (7) 



(«). 



(0\ 



(/, Q-no + BiQ/^ + B,Q',Jl'+. 



for the potential at any internal, and iw~.*ffi,^\ for the 

potential at any external point 
The whole potential, then, will be given by 

at any point external to both spheres. 

Also V-4ira^^A*,M + 4ir^*(A*',p) inside a; und 

V-4»^^/'M,^) + 4W/,y) inside b. 

Now, the conditions of the problem require that the values of 
y in the two last cases shall be constant Our functions are, there- 
fore, to be determined by the equations 






(8), 



which are to be satisfied with obvious restrictions on r and r^ in each 
case. Ite verting, however, to the expressions (o), (/3), (y), &c., we 
see that we need not solve the problem in the general form thus 
suggested ; for it will be sufficient if we determine the constants 
Ao, Aj, &c., Bo, Bj, &c. Now, if we make/i=l, /I'-l,— that is, 
consicler only points on the central line, — then Q^^l, Q^— 1, &c., 
Qi'=l| Q«'"l» *c.^ A^, Aj &c. Bo, Bj, &c., are the coefficients 



&c., and 



_b 



, &c., in the expressions for the 



(.). 



of — » — » 
r\ r\ 

potentials inside the spheres a and b. Hence, if / ( L ) and 

F (^\ denote the values of ^ ( ;*,- j , « (f^'X) • when fi - 1 
and /i'^1, we need only solve the equations 

where we have replaced r and / by their values c - / and c-r^ e 
bein^ the distance between the centres of a and b. Poisson then 
eliminates the function F, by choosing a new variable (, such that 

r^ — , and remarks that we may give to ( any value between 

+ a and - a, and therefore we may write r for f ; we thus have the 

same variable in both the equations, and F ( j which occurs in 

both may be eliminated. The result is 

„/(£)+^_/CJ!£rf!L).A.^, . .(0. 

\a J c^-b*-cr \<r-b*-crj e-r 

Tills is the functional equation on which depends the solution of 
the problem of two mutually iuduencing spheres. 

Poisson treats very fully the case of two spheres in contact ; for 
which case, taking a — 1, the above equation oecomes 

^''"^ "ft+O + dKl-r/Vft+Cl + ^Xl-r))" ^ "f+6^ • • ^''^ 

^ We are, of coarse, assuming aquaiutanoo with the properties U 
spherical harmonica. 



32 



ELECTRICITY 



[ELKCfTBOSTATXCAL THSOET. 



He fincb a aolation, 



Plana 

and 

Roche. 






(14*Xl-r) 



CU, . (0). 



It 18 then easy to find ¥{r\ and write down the general expressions 
for the potential. Poisson goes on to show that the density at 
the point of contact of the spheres is zero. He finds, for the 
mean density on the two spheres 1 and b respectively, 

1 1 



A 






this being, in fact, the value of / (0), 



andB 



b{\'¥h)J 1-t 



He shows that the calculation of the ratio ;B of A to 6 may be 
reduced to the calculation of the first of these integrals only. For 
the difference 4ir62B-4irA between the charges on 1 and h he 
finds the elegant expression 



1 + 6 



cos 



1+6' 



Sjmthe- 
tical me* 
thodof 
Green. 



from which it follows that the whole charge is always greater 
on the sphere of greater radius. He then calculates the value of /3 
for various values of 6, and its limit for 6—0, and next the ratio of 
the densities at the two points diametrically opposite the point of 
contact, and finds for tne mean density on each of two equal 
spheres in contact A— A log 2. He also calculates for this last 
case the ratio of the greatest to' the mean density. In the case of 
two unequal spheres, the ratio of the greatest density on the smaller 
to the mean density on the larger, is found for various values of 6. 
He then passes on to investigate the densities for various values 
of /&. 

All these results are compared with the measurements 
of Coulomb, and found in satisfactory accordance with 
them. In his first memoir, Poisson considers the case 
where the distance between the spheres is great compared 
with the radii ; and in a subsequent memoir he considers 
the case of two spheres at any distance. 

Plana {Sur la distribution de Velectricite d, la surface des 
deux Sjphh-esy Turin, 1845) extended the calculations of 
Poisson, using much the same methods. He also calcu- 
lated approximately the mean densities in the case of 
several spheres in contact, and arrived at results which 
agreed satisfactorily with the experiments of Coulomb. 
For a table of his results, see the end of the first volume 
of Riess's Reibungselectricitdt An account of the work 
of Roche, who also followed in the footsteps of Poisson, 
will be found in Mascart, t i. p. 290 sqq. 

The researches of Green led him to a very valuable 
synthetical method, by means of which we can construct 
an infinite number of cases where we can find the electri- 
cal distribution. Suppose that we take any distribution 
whatever of electricity, for which we know the potential at 
any point, and consequently the level surfaces. Take any 
level surface, or parts of level surfaces, inclosing the whole 
of the electricity, and suppose these level surfaces to 
become actual conducting sheets of metal. Suppose the 
electrical distribution inside to be rigid, and connect the 
sheets of metal with the earth, so as to reduce them to 
potential zero. The sheets will become charged in such a 
way that the whole potential at every point in them and 
external to them is zero. Let now U be the potential at 
any external point due to inside distribution, and Y that 
due to the charge on the sheets, then we have everywhere 
on or outside the sheets, U + V = 0, or V = - U. Now U 
is constant at every point of each sheet ; hence Y is so 
also. Hence the distribution to which Y is due is an 
equilibrium distribution per se. Removing now our internal 
distribution, and changing the sign of that on the sheets, 
we have a distribution of electricity in equilibrium on a 



set of conductors of known form, the potential of which at 
any external point is YbU, where U is known. Also 
the potential Y Lb clearly constant inside every conductor. 
Hence, applying the characteristic surface equation, we get 
for the density at any point of any of our conductors tiie 
expression 

•-_JL ^ 

4ir dy 

We might make this a little more general, and state our 
result thus : — If we distribute on a level surface or sur^ 
faces of any electrical system^ completely vidosing that 
system^ electricity vnth surface density at every point 

o" = - T — J- , this distribution will of itself be in equUi- 

brium, and the potential at any external point will he kJJ, 
We have given a physical demonstration of this import- 
ant theorem. The mathematical reader will easily see the 
application to this case of the general reasoning about the 
solution of V^V = 0, of which we have already given 
examples. For a simple but interesting - case of this 
general theorem, see Thomson and Tait's Natural Philo- 
sophy, voL L § 608. 

To Sir William Thomson we owe the elegant and Hetl 
powerful methods of "Electric Images" and " Electric ^[^ 
Inversion." By means of these he arrived, by the use of .^^ 
simple geometrical reasoning, at results which before had q^ 
required the higher analysis. We shall endeavour toimag 
illustrate these by two simple examples. We do not 
follow the methods of the author (for which, see his 
papers), but take advantage of what we have already laid 
down. 

Let A be any point outside a sphere (fig. 12) of radius a, and 

centre C. Let kC^f and take B in CA 

' ' • a« 

such that CBCA=a«, or CB=y; then it 

is easily proved that, if P be any point on 
the sphere, 

BP a 




AP / 
Hence if E be any quantity of electricity, we have 



Fig. 12. 



_5. 
AP 



BP 



0. 



Therefore, if we place a quantity £ of electricity at A, and a quaa- 

d 
tity - -^E at B, the sphere will be a level surface of these two, that, 

namely, for which the potential is zero. Another level surface of the 

system is evidently an infinitely small sphere surrounding A. 

Hence it follows, from the theorem of Green which we have just 

discussed, that a distribution of electricity on the sphere, the 

■p 

density of which is given by <r="7- (where R is the resultant force 

due to E and - ^ E at any point of the sphere), together with a 

quantity E at A, gives a system in equilibrium, the potential due to 
which at any point outside the sphere is the same as Uiat of £ at 

A, and _ -^EatB. 

It appears, therefore, that the action of the electricity 
induced on the uninsulated sphere by the electrified point 
A is equivalent at all external points to the action of 

- ?E at B. The electrified point B is called by Sir Wil- 
liam Thomson the electrical image of A in the sphere. It is 

obvious that the whole charge on the sphere is - ^E, and 

we can very easily find the density at any point 

In fact, resolving along CP, which we know to be the dinotfoB 
of resultant force, uie forces dae to A and B, we get 

~—E 
B-jJi««'CPA-/piCO.CPB 



KLICIBOSTATIOAL IBKOBT.] 



ELECTRICITY 



E / u'4-A 



/E 
-a"AF 






i)E 



■ («). 



We might hftve any nnmber of external points and find 
the image of each. We should thus get a system which 
might bo called the image of the external system. The 
distribution induced in an uninsulated sphere by such an 
eiternal system could easily be foand by adding up the 
effect of each external element found by means of its 
iniage. Similar methods might also be applied to an in- 
ternal system. The solution can be generalized without 
diflicaity to the case where either the charge or potential 
of the sphere is given. 

Suppou the chikTge Q given ; superpose on the dutribation fonnd 
ibota s nniform diitribntion ot amount Q + ; E. Tliia will pro- 
duce > constsnt poienti«l ^ + t all over the sphere, and therefore 
will not distnrb the eiimUbrinni. We have thua got the reqnired 
dittribntion of the given charge Q under the influence of A. Tlie 
dnisitf of any point is given by 

„=_Q4.^ t/*-"''^ (41) 

4«j'*4ia^" 4wAP 

B So far the method of images is simply a synthetical 
method foe obtaining distributions on a sphere. But Sir 
William Thomson has shown us how to convert it into an 
instrumeut for ininsfuiming any electrical problem into a 
variety of others. 

If P be any point {fig. 13), a fixed point, and F bo taken 
in OP such that OP.OP' = a», o 

then P* is called the inverse 
of P with respect to 0, which 
is called the origin of inver- 
sion, or simply the origin; a 
is the radius of inversion. We " v " ' 

may' thus invert any locus of '* ''■ 

points into another locus of points, which we may call the 
inverse of the former. 

Let P, Q and P, (f be any two points and their inreraea. Let na 
HpKHe that there is a charge E at Q, and > charge E* at Q', which 
is tke image of E in a sphere with ndiua a and centre O ; so that 

K- aqE . Let V and V be the respective potential* of E and E' 
iX P and P'. Then we have obvioualy 



It ia ver; eaay to show that, li di, dS, 
_.,.,„_.. . to of length, iorfsce, and volume, and aurface and 
T^ome densitiea, and the same sjnibola with dashes the inverses ot 
thMB, then we have 



By means of these equations it is easy to invert any 
electrical system. Take, for example, the case of any con- 
ductor in electrical equilibrium ; tiien, since its potential 
is everywhere constant, it inverts into a surface distribu- 
tion, the potential at any point of which distant r' from 

the origin is by (42) -> C, where C is the constant poten- 
tial of the conductor. The surface density at any point of 
the system is found from that of the corresponding point 
on the conductor by the equation 



' For the general propertiea of enrvH and their invenea, the reader 
may eonault Salmon a Solid Oeowittry, He will hare no dUSenltj i& 
|«xiTJng for hlnuelT ancb a« we shall roqnirs Lara. 



-p,'- 



Again, if we consider the system thus found, it is obvious 
that, if we place a quantity -aC of electricity at the 
origin, this will make the potential at every point of the 
system zero, and we have a solution of the case of an 
uninsulated conductor, whose surface is the inverse of that 
of the given conductor, nnder the influence of an electrified 

As an example of the use of this method, let us invert the tml- 
form diatribution od a sphere with respect to an origin on its cir- 
cumference, the radius of inveision bein^ the diuneter of tha 
ipbere. The sphere inverts into an infinite plane, touching at 
the other end A nt the diameter through the ongin. Let C be the 

potential on the sphere so that " — aZj • where d a the diameter. 
Hence the density at an^r point P on an infinite plane influenced by 
* qnantity - Cd of electricity placed at a point O distant d from it 



Again, inverting points inside the sphere, for which the poten- 
tial IS constant, we get the potential due to the diatribution on the 
infmiCe plane, at points on the other side from the inducing point, 
the reenlt being 



which is the same as that due to dO at 0. Hence tha potential at a 
point on the same side as O is that due to a qoanti^ d{' placed at 
(T, where (TA-OA. 0* is in fact the image of O. If we write Q 
tor - Cd, then wa get 



(43). 



These results might of conns have been deduced as particnlsr cases 
of a sphere and point. 

Many beautiful applications of these methods will be 
found in the Reprint of Sir William Thomson's papers and 
in Maxwell's Medricily and Magnetitm. Two of these are 
of especial importance. Adopting the method of sncces- 
sive influences given by Murphy {EUdrieity, 1833, p. 93), 
and conjoining with it the meUiod of images, Sir William 
Thomson treated the problem of two spheres. For his 
results, see Reprint, pp. 66-97. At the end of that paper 
two valuable tables are given — L " Showing the quantities 
of electricity on two equal spherical conductors of radius 
r, and the mutual force between them, when charged to 
potentialsu andvrespectively ;" II. " Giving the potentials 
and force when the charges D and £ are given." The ratio 
of u to D in the first case and of D to E in the second is 
also given, for which at a given distance there is neither 
attraction nor repulsion. An interesting experiment on 
this curious phenomenon is described in Riess, Bd. i. 
j 166. For an application of dipolar co-ordinates to the 
problem of two spheres, see Maxwell 

Thomson also applied his methods to determine the die- Spbstkal 
tribution on spherical bowls of different apertures. See ^■o*'- 
Seprini, p. 178 sgq. His numerical results on p. 186 
are extremely interesting, as affording a picture of the 
effect of gradually dosing a conductor, and are of great 
value in giving the experimenter an idea as to what aper- 
ture he may allow himself in a vessel which he desires 
should be for practical purposes electrically closed. 

It wonid lead us too far to discuss here the analytical Conjn- 
metbod of conjugate functions, and the alhed geometrical ^** 
method of inversion in two dimensions. A fall account of ^^ 
these, with important applications, will be found in Max- 
well, voL L S 182 sqq. 

We shall conclude our applications with a brief notice 
of a few of the ordinary electrostatical instruments, refer- 
ring the reader for an account of some others to the article 

ELicTBOKRKE. 

If two plates be placed parallel to each other, and one 
VIU. - s 



34 



ELECTEICITT 



[blectbostaticai. thkobt. 



r«nllBl of them raised to potential V, while the other is connected 
(l«l«a. with the earth, then there will be certain charges E and F 
on the two plates. If p and r be the coefficients of self- 
induction for A and B, and q the coefficient of matnal induc- 
tion, then in the present case 

E-pV, F=g7, 
and the energ; of the distribution is obviously 

Q = iEV-ipV', 
80 that the work done by completely discharging the con- 
denser aV*. If we suppose the plates very lai^ com- 
pared with the distance between them, then we may 
treat the case, for all points not very near the edge, as if 
the plates were infinite. 

In thU case the liaes of force Bt« straight, and the nuDber of 
lines of force which leave any area on A is equal to that of those 
which enter the opposite area on B. Hence ths surface densities on 
the plates are eqnal and opposite in sign. Also we clearly have 



'-ii-iir <">■ 

For the number of lines of force which cross sny Unit of srea parallel 
to the plates is constant, anil therefore the resultant force ia con- 
stant at every point between tho plates. 
MndpU I' appears, therefore, from (44) that if we make the dis- 
•f iwo- tance between our plates very small, the density on the 
""I*' inner surface will be very great, and the whole charge on 
A very great. An apparatus of this kind for collecting 
large quantities of electricity at a moderate potential is 
called an accumulator or condenser. One of the first instru- 
ments of this kind was Franklin's pane, which consisted 
of two sheets of tinfoil pasted opposite each other on the 
two sides of a pane of glass. There is of course a practical 
limit to the increase of capacity in such arrangemeats, 
because a spark will pass when the insulating medium is 
too thin. The greater dielectric strength of glass makes it 
more conTOnient than air for an insulating medium, and 
we shall see by-and-by that it has other advantages as well. 
YThen the plate A is of finite size there will in general be 
a distribution of electricity ou the back comparable with 
the charge which A would hold at potential V if B were 
absent. When the dbtance between the plates is small, 
by far the greater portion of the capacity is due to the 
Coodsns- presence of B. Advantage of this principle has been taken 
Ins in the condensing electroscope of Volta, which is an ordin- 
"'*''"■ ary gold-leaf apparatus, except that the knob is replaced 
""^ by a circular disc on which is placed another disc fitted 
with an insulating handle ; the discs are covered with a 
thin coat of varnish which serves as an insulating mediuna. 
If we connect with either disc, say the lower, a source of 
electricity of feeble potential V, and connect the upper 
disc at the same time with the earth, then a large quantity 
of electricity at potential V collects on the lower disc. 
Now remove all connections, and lift away the upper disc 
The capacity of the lower disc is thereby enormously di- 
minished. Therefore, since the charge is unaltered, its 
potential must rise correspondingly ; and the gold leaves 
may diverge very vigorously, although a simple connection 
witii the lower disc alone would scarcely have moved thorn. 
This instrument is of great use in all cases where we have 
an untioiited supply of electricity at feeble potential Sir 
Qani William Thomson has devised an accumulator of measur- 
ling able capacity, called the Qnard Ring Accumulator, which 
J°°'^''' is a modification of the arrangement we are discussing. 
*^' AB (lig, II) is a flftt cvlindrical metal box, the upper end oT 

which is truly plane, and hu a >. 

eircnlar aperture, into which 
fits, without toncliiiig, a plane 

disc C, which is snpported on » |J k_ 

the bottom of the boi by in- . c 

snlttting 8upport«,_ so that its I [j P 

Dpper surface is in the same ) I i I 

plane with the lid of the box. 
D£ i) a metal disc which can 
bemoTMlby a 



PIg.1*. 
throiuh msanuod distancfla, alwayi renuining 



parallel to AB. When desired, C can be put in eommanication 

with AB. It may then be reguded w fonnincF part of an infinite 
plate, so that if AB be at potential V, and D£ at potential Ttn, 

then the snrTace density on C will bo equal to-r-j , where il u the 
distance between the plates ; and if A be the ai«a of C the whole 
amount of electricity on C is t^ ■ If now we break the oonnec- 
tion between C and the boi and discharge the box, we are left with 
a known qnantity of electricity on C, viz. -7-5 . 

The most nsual and for many purposes the most con- Lards 
venient form of accumulator is the Leyden jar. ThisisJ"- 
merely a glass jar (fig. 16) coated to a certain height ont- 
side and inside with tinfoil. The mouth 
of the jar is stopped with a cork or 
wooden disc, which serves the double pur- 
pose of keeping dirt and moisture from 
the uncovered glass inside, and of carrying 
a wire in metallic connection with the 
inside coating, which passes up through 
the stopper and ends in a metal knob. If 
the glass of the jar be very thin, we may 
find the distribution on the two coatings 
by neglecting the curvature ; the electric , 
density on the inner surface of the two 
coatings will then be the same as in the ^B- ^^ 

case of parallel plates. If, therefore, the inner coat- 
ing be at potential V, and the outer at potential zero, 
the density on the inner coating will be j-, > aiid that on 
the outer - j-j . In the particular case we are consider- 
ing the inner coating forms very nearly a closed condactor, 
so that there will be very little electricity on its inner sur- 
face, and there will also be very little on the wire and 
knob compared with the amount on the surface of the inner 
coating which is next the glass. We may therefore put 
for the whole electricity on the inner coating -r-^, where 8 
is the extent of its surface. The capacity C of the jar is 
then given br 




{«). 



Green calculated to a fir^t approximation the effect of the enm- 
ture on the capacity, and found that, if R sjid R' be the greatest 
and least radii of curvature of the inner coating at any point, then 
the densities on the inner and outer coatings are given by 

U<hk)] ■■■■ "* 

and consequently the capacity of the inner coating by 

In any case, C being a constant, we have charge £ ^ CV Battoi 
and energy Q = JCV*. Hence if we connect the inner "f^" 
coatings of n similar jars, and charge them to potential V, '^^ 
all the outer coatings being at the same time connected 
with the earth, we have, E and Q representing the whole 
charge and energy, 

E-nCV 1 
Q = |cV.i ("^ 

If we dischai^ such a battery of n jars into another of 
n' similar jars, by connecting the knobs together, and the 
outer coatings to earth in each case, we have, U being the 
common potential after discharge, 

nCV-wCU-l-n'Cn 

and TJ-^.V («). 

Thare Is therefore a loss of energy represented by 



XLlCrrB08Tl.TXGJLL THXO&T.] 



ELECTRICITY 



35 



In other words, an -T~-/th part of the potential energy 

is lost. When a battery of jars is discharged through a 
circuit in which there is a fine wire of large resistance, 
the greater part of the potential energy lost in the dis- 
charge appears as heat in the fine wire. Riess made 
elaborate experiments on the heating of wires by the dis- 
charge in tliis way, and the results of his experiments are 
in agreement with the formulae which we have just given. 
(See Heating Effects.) 

ttery We may also arrange a battery of jars by first charging 

9tiit%, each separately to potential Y in the usual way, and then 
connecting them in series, so that the outer coating of each 
jar is in metallic connection with the inner coating of the 

/ next. In such an arrangement of jars, it is obvious that 
in passing from the outer coating of the last at potential 
zero to the inner coating of the first, the potential will rise 
to nV. When we come to discharge such a series, the 
electromotive force to begin with is nV, so that for any 
purpose in which great initial electromotive force is 
required this combination has great advantages over n jars 
abreast. The '' striking distance," for instance, t,e., the 
greatest distance at which the discharge by spark will just 
take place through air, is much greater. On the other 
hand, the quantity of electricity which passes is less, being 
only CV instead of nCV ; the whole loss of potential energy 
in a complete discharge is, however, the same. 

The case which we have been discussing must be care- 
fully distinguished from that of a series of jars charged by 

^gc»de. ''cascade,'' where n uncharged jars are connected up in 
succession as in last case, and the first charged by con- 
nection with the electric machine to potential V, while the 
outer coating of the last of the series is connected to earth, 
and the rest of the jars insulated. The whole electro- 
motive force in this case is clearly only V, and, if all the 
jars be similar, the potential difference between the coatings 

in each is — ; the charge on the inner coating of the first is 

CV CV 

therefore — -> and the whole potential energy only A — . 
n n 

The arrangement is, therefore, not so good as a single jar 

fully charged by the same machine. It was fancied by 

Franklin, who invented this method of charging, that some 

advantage was gained by it in the time of charging, the 

notion being that the overflow was caught by the successive 

jars and that electricity was thereby saved. Charging by 

cascade was treated by Qreen. Some of the experiments 

of Riess bear on the matter (vide Mascart, §§ 190, 191), 

which, after all, is simple enough. 

f^ fj^ In the theory of accumulators, or condensers as they 

Hmd cure often called, much stress has been laid on the differ- 

•c- ence between '*/ree" and ** 5<mmi" electricity. To illus- 

^^« trate the meaning of these terms, let us tpke a case where 

the calculations can be carried out in detail 

Sappose we have two concentric spherical shells, an inner, A, and 
an outer, B. Let the outer radios of A be a, and the inner and 
outer radii of B be 6 and e, so that the thickness of the latter is 
c~b. We riiaU suppose that we can, when we please, connect the 
inside sphere with the earth. It is clear that there can never be 
any electricity on the inner surface of A. Let the charges on the 
other surfaces in order be E, F, G. Let us suppose in the first in- 
stance that A is at potential Y , and B at zero. Tnen we have to find 
£, F, 0. Draw a surface in the substance of B; no lines of force cross 
it, therefore the whole amount of electricity within is zero. Hence 
F* - E. Also, considering the external space, which is inclosed 
between two snrfibces of zero potential, we see tha^ O— 0. Thus, 

E B 
since A is at potential Y, we have - _ t-^* 



E - j^ V -i>Y f where i)-^ "j 



.(51). 



In this case, then, there is no electrification on the outiide of B, 
tad an electrio pendnlom suspended there would give no indication. 



Let us now connect A with the earth, so that its potential becomes 
zero ; we have now to find the charges and potentials, our datum 
being that the whole charge on B is - E . 

As before, we have F— - £', but Q is no longer zero. We have, 
however, F+G'^-E. Hence G'-E'- -E. 

■joi pjf rtf 

Also, since A is at zero potential, - - ^ j — —0 . 

a 6 c ' 

therefore G' - .^^ ; - F- E'- ^^ ; G'-:^- . 

p p+c p+e 



The potential of B is 



C p + C 



cp 



In this process, therefore, a quantity E - E', or -~- Y, of electri* 



p + c 



-cp 



city has flowed away to earth from A, and a quantity — -^ Y haa 
passed &om the inner to the outer surface of B, while the potential 

has altered, on A from Y to 0, and on B from to — ^ Y. 
* ' p + c 

Suppose now we connect B with the earth, thus reducing it to zero 

potential. Since the charge on A remains the same, and that on 

the inner coating of B is equal and opposite to it, it follows that 

now the charges on A, &c., are -— Y, -^ Y, 0, where q denotes 
-— ; and the potentials of A and B are - Y and 0. After another 
pair of such operations the charges will be ^ -^ Y, ^tc, and the 



c c 



potential,-^ 



Y ; after a third, charges, 



7 l\^' 



&c., and potential. 






jY . Hence the charges and potentials go on decreasing in geo- 
metrical progression.^ Amounts of electricity flow away from A 
equal to gY, gj Y, q^ V, q^*Y &c., in the successive operations, 

and equal amounts of opposite signs are discharged from B. The 
sum ot all these discharges is the whole original diarge on A, for 



?v( 



^ C C 



+ &c., ad, \nf,\ --2-^ V-i>Y. 



Hence by an infinite number of alternate connections 
we shall finally discharge the jar completely. The elec- 
tricity which flows out at each contact is called the ^ free 
electricity," and that which remains behind the '' bound 
electricity." The quantity which we have denoted by p Capacity 
is clearly the capacity of a spherical Leyden jar ; it in- of tpheii- 
creases indefinitely as the distance between the conduct- ^ i*'* 
ing surfaces decreases, and is very nearly proportional to 
the surface of the inside coating, when the distance is 
small compared with the radius of either surface. 

It is very easy to extend our reasoning to any con- 
denser. 

If, in fact, ?iif ?ii« 9aa be the coefficients of self and mutual in- 
duction for the armatures, then this potential after operating n 

times u above b (^J"v, the cIuigM, «u(j,^^)"v and 

/!,.( -iiX I y. and the amounts of eleetricitr wUch lesTS I 
""Vfiiftt/ _ . \/ 1 \ 

and 2 in the nth operati^x «e ±Wa ( ^"j['*gj" ) [^^ ) V 
respectively. 

We must not omit one more interesting case. If we Coaxial 
have two infinite coaxial cylinders of ludii a and J cylinder* 
(6 > a), then obviously the potential is symmetrical about 
the common axis, and Laplace's equation becomes 



iPY IrfY 



The integral of this is Y-C log r+D. Let the inner cylinder 
be at potential Y^ the outer at potential Y„ then 

Heno* the ■azfaee density on the inner cylinder is gtTen by 

1 dV 



llllx 



•-r 



36 



ELECTRICITY 



[tHB DISI«£CTRia 



and the capacity per unit of length of same is 

1 

7~' — * ' * 

2a Log a 



. (53). 



This result has important applications in the theory of 
telegraph cables, and to a form, of graduated accumulator, 
invented by Sir William Thomson, and used by Messrs Gib- 
son and Barclay in their experiments on the specific induc- 
tive capacity of paraffin (see Maxwell, vol L § 127). 

ON THE INSULATING MEDIUM. 

It has been assumed hitherto that the medium inter- 
posed between the conductors in the electric field is in 
all cases air — the most prevalent of all dielectric media ; 
or, where any other medium actually occurred, as in the 
case of the Leyden jar, it has been assumed that the 
result is the same as if the glass were replaced by air. 
Experimenters soon recognized, however, that the capa- 
city of a Leyden jar depends very much on the quality of 
the glass of which it is made. But the nature of this 
action was very little understood, until Faraday showed by 
a number of striking experiments that the dielectric has a 
specific function in cdl phenomena of induction. 

Fara- Faraday used in his experiments two identical pieces of apparatus, 

day's which were virtoallj two spherical Leyden jars. The outer coating 
experi- EF (fig. 16) was divided into two hemispheres, which could be 
nient^ fitted together air-tight The lower 
hemisphere F was fittM to a perforated 
stem, provided with a stop-cock G, so 
that it conld be screwed to an air- 
pump while the apparatus was being 
exhausted, and afterwards screwed into 
a foot H. The upper hemisphere was 
pierced by a tube, into which was 
cemented a shellac nlug B. C is a 
metal wire passing aown through B, 
which supports the noUow metal sphere 
D, forming the inside armature, and 
carries the metal ball A, by means of 
which D can be charged and discharged. 
To give an idea of the size of the ap- 
paratus, it may be mentioned that tne 
diameters of the inner and outer 
spheres were 2*33 in. and 3 '57 in. re- 
spectively. Two jars were made on 
the above pattern, as nearly alike as 
possible. The equality of tiieir capa- 
cities was tested as follows. Both were 
filled witii air at the same temperature 
and pressure. Apparatus I. was then 
chaiged, by bringing A in communica- 
tion with the luiob of a Leyden jar, 
while the coating EF was connected 
to earth. I. and 11. were then placed at 
a moderate distance from each other, as Fig. 16. 

symmetrically as possible with respect to the observer and other 
external objects, the outer armatures in both cases being in con- 
ducting communicatioa with the earth. The ball of I. was touched 
by a small proof sphere, the repulsion of which on the movable 
ball of a Coulomb balance was measured; after a short interval this 
measurement was repeated. The balls of I. and II. were then 
brought into communication, and the charge divided between the 
internal armatures. The ball of II. was immediately tested as 
before, and then the ball of I. again. Finally I. and II. were 
dischajffod and tested for permanent *'stem efiect" The result of 
one such series of measurements was 




I. 

XL 



0. 



254,250 



122 



124 1 1 



Neglecting the slight dissipation of the charge, and taking 
account only of the "stem efiect" in I., we see that Uie chaxges on 
I. and II. after division are represented br 122 and 124, each 
of which is not far from the half of the whole disposable charge in 
I., viz., 124*5 ; so that the capacities of the two jars must be 
oqoaL This wiU perhflf[>s be clearer if we consider wliat would 
happen were the capacities une<}ual. Let the capadtiet be and 
C, thepotenlial of i. before division Y, and the common potential 
after U, the chaise on I. Q, and on I. and II. q and 9^ after 
division. Then Q-CV, g-CU, ^-CTU, and «+/=Q. The 
iBdxcation of the tonion balance is proportional to tne dmge of 



the proof sphere, that is (owing to the symmetry of the arrange- 
ments), to tne potential of the knob with which it was in contact ; 
or at all events this is true if we consider only readings taken from 
the knob of the same jar, and that is all we shall ultimately want 
But(C + C)U-CVi hence 

c" U 

Hence the ratio of the capacities is equal to the ratio of the excess 
of the first over the last reading to the last reading, both being 
taken from the knob of I. Thus, taking the uncorrected values 
in the above experiment, the ratio of the capacities would be 
(250-124)-r-122, i.e, 1'02. By various experiments of this kind, 
Faraday convinced himself of the equality of his two jars. To 
test the sensibility of his method, he reduced the distance between 
the lower hemispheres and the ball in II. from '62 in. to *435 in., 
by introducing a metal lining. The capacity of II. was then 
found to be 1 '09 (the mean of two observations). He next com- 
pared the capacities of the jars when the lower half of the space 
between the armatures of one of them was filled with shellac. 
The ratio of the capacities was found to be 1 '5 (mean of several 
experiments), the shellac jar having the greater capacity. 

It appears, therefore, that, other things being equal, the Spedlk 
capacity of an accumulator is greater when the insulating indncci 
medium, or, as it is called, the " dielectric," is shellac, **P*<** 
than when it is air. The ratio of the capacity in the 
former case to that in the latter^ is called the Specific 
IiidtLctive Capacity of shellac This we shall in general 
denote by E. According to this definition, air is taken 
as the standard, and its specific inductive capacity is 
unity. Properly speaking, we ought to state the tem- 
perature and pressure of the air ; we may assume 0° C. as 
our temperature, and the average atmospheric pressure 
(760 mm.) as our standard barometric pressure. 

It is easy to obtain an approximate value of K from the 
above result for the shellac apparatus. Remembering that 
the shellac occupies only one hemisphere, and assuming 
that the lines of force are not disturbed at the junction of 
the air and shellac, we have, if p denote the ratio of the 
capacities, 

j^jjY--p, audK-2p-l . 

This gives for shellac K = 2*0, the real value being pro- 
bably greater. Similar experiments gave for glass and 
sulphur K = 1'76 and 2-24 respectively. 

Thus the specific inductive capacities of shellac, glass, 
and sulphur are considerably larger than that of air. 
Faraday was unable to find any difference in this respect 
between the different gases, or in the same gas at different 
temperatures and pressures, although he made careful 
experiments in search of such differences. 

It would lead us too far to discuss in detail the pre- 
cautions taken by Faraday to remove uncertainty from his 
experimental demonstration of the existence of a specific 
dielectric action. The reader will find a minute descrip- 
tion in Faraday's own surpassingly lucid manner in the 
eleventh series of the Experimental Researches, 

His discovery of the action of the medium led Faraday 
to invent his well-known theory of the dielectric. Ac- Fan- 
cording to him, the fundamental process in all electrical day's 
action is a polarization of the ultimate particles of matter ; ^^^^^ 
this polarization consists in the separation of the positive 
and negative electricities vAthin the molecules, exactly as 
the two magnetic fluids are supposed to separate in the 
theory of magnetic induction. In this view a dielectric 
is supposed to consist of a number of perfectly conducting 
particles, inmiersed in a medium or menstruum, which is 
either a non-conductor or a very imperfect conductor. 
When electrical action starts, the two electricities separate 
in the molecules ; but, in the first instance at least, there 
is no mterchange of electricity between different molecules. 

^ It must be noticed that the assumption is tacitly made that the 
air Li to be replaced by shellac everywKert^ or at least wherever there 
•re lines of force. 



THB DIXLICTRia J 



ELECTRICITY 



37 



Faraday assumed that the electrical action is propagated 
from molecule to molecule by actions whose sphere of 
immediate activity is very small. He denied the existence 
of '* action at a distance," and regarded his results about 
induction in curved lines as at variance with it. Thomson' 
showed, however, that Faraday s results were perfectly 
consistent with the theory of action at a distance, pro- 
vided the polarization of the dielectric be taken into 
account, and that the mathematical treatment of the 
subject is identical with Poisson*s theory of induced 
magnetism. The theory of action at a (^stance as ap- 
plied to this subject will be found under Maonetism. 
Helmholtz, whose memoirs we ha* already mentioned, 
takes this view of the matter. We do not propose to 
follow Faraday's theory any further at present ; its main 
features are involved in Maxwell's theory, to which we shall 
afterwards allude. 
Dens. W. Siemens^ examined and confirmed the conclusions 
of Faraday. He used voltaic electricity in comparing the 
capacities of condensers. By means of a kind of self-acting 
commutator^ (Setbstthdtige Wippe\ the armatures of the 
condenser were connected alternately with a battery of 
Daniell's ceUs and with each other; so that the condenser 
was charged and discharged about 60 times per second. 

Figure 17 gives a scheme of the arrangement. F and are two 
insulated metal screws, ^ 
with which the yibrat- 



wicn wmcn uie yiorai- ^ 
in^ tongue £ of the f ^ 




Fig. 17. 



Wipne comes alter- 
nat<>ly into contact ; 
CD und AB are the 
armatures of the con- 
denser, H the battery, 
and K the galvano- 
meter. Theory indicates, and experiment confirms, that the deflec- 
tion will be the same whether the snJvanometer is put in the 
char^ or in the discharge circuit The former arrangement is 
that indicated in the figure. 

The amount of electricity which flows through the 
galvanometer each time the condenser is charged, is pro- 
portional to the product of the capacity C of the condenser 
and the electromotive force E of the battery. £ is propor- 
tional to the number of cells in the battery. If, therefore, 
the speed of the Wippe be constant, the galvanometer 
deflection, or its sine or tangent as the case may be, will 
be proportional to EC. By varying E and C inde- 
pendently, we can verify the laws that regulate the charge 
of condensers. If we keep E the same, and the speed the 
same, we can compare the capacities of two condensers, or 
of the same condenser with two different dielectrics, and 
thus find the specific inductive capacities of various sub- 
stances with respect to air. Siemens found tliat C is 
independent of £, and concluded that the effect of solid 
dielectrics on the capacity of a condenser is not to be 
explained by a penetration of the electricity into the 
dielectrica We shall give some of his values of the specific 
inductive capacity farther on. 

Gaugain^ studied the effect of the insulator on the 
capacity of condensers. He used in his researches the 
discharging electroscope (see art Electrometeb), an in- 
strument which does not at first sight look likely to lead to 
very accurate results, but which seems to have worked 
satisfactorily in his hands. Many of Qaugain's results 
concerning the gradual increase of the charge are very 
interesting ; their bearing on theory is difficult to estimate, 
however, owing to the mixture of effects due to surface 
and body conduction. His results concerning the "limit- 

^ Camh. €und Dvh, Math. Joum., 1845, or JteprirU of Papers ^ p. 15. 
« Poifg. iiim., ciL, 1857. 

' For a description of this instrument, see Wiedemann's QaUxmitrnMB^ 
Bd. L i 451. 
« Aim, <U Ckim, tt de Ph^$., 4 ser. t iL (1862). 



ing " value of the specific inductive capacity are at variance 
with those of subsequent experimenters who have worked 
with more delicate instraments. 

In their experiments on the specific inductive capacity Oibsoa 
of paraffin, Qibson and Barclay^ employed a method due to *°<^ 
Sir William Thomson, in which an instrument called the ^^y* 
Platymeter is used in conjunction with the quadrant elec- javitr. 
trometer. They found for the specific inductive capacity 
of paraffin 1*97, and showed that this value alters very 
little, if at all, with the temperature. 

The most extensive measurements of this kind that have 
been made of late are those of Boltzmann * and Schiller.^ 
Boltzmann used a sliding condenser, whose plates could be ^'ts 
placed at measured distances apart Plates of different '""^ 
insulating materials were introduced between the parallel 
plates of the condenser, so as to be parallel with them and 
at different distances from one of them. 

According to the mathematical theory, the capacity of the con- 
denser is independent of the position of the plate, and yaries 

inversely as m - n + ^ , where m is the distance between the 

plates of the condenser, and n the thickness of the plate of insulat* 
mg material whose specific inductive capacitv is K. In other wordi^ 
the plate may be supposed replaced by a plate of air of thickness 

»-. If therefore A denote in absolute measure the reciprocal of the 

capacity of the condenser, then 



\ = Q(m-n+ g-j ,' 



where Q is a constant The capaci^ of the condenser was mea- 
sured by charging it with a battery of 6 to 18 Daniell's cells, and 
then dividing its charge with the electrometer. One pole of the 
battery and one armature of the condenser are connected to earth. 
The other pole of the battery is first connected with the electrode A 
of the electrometer, whose other electrode B is connected to earth. 
Let the reading thus obtained be £, then £ is proportional to the 
potential of the battery pole. The condenser is next charged by 
connecting its insulated armature with the battery; the batteiy 
connection is then removed, and the electrode A of the electrometer, 
which has meanwhile been connected with the earth, is now con- 
nected with the condenser. If C be the capacity of the condenser, 
C that of the electrometer (in certain cases artificially increased), 
we have, if F be the common potential of the condenser and con- 
nected parts of the electrometer, (C + C)F=.CE, and 



C = 



E-F 



or A. = 



E-F 



1 
C 



But F is proportional to the second reading of the electrometer, 
hence A. is known in terms of C. As only relative measures are 
wanted, C is not required. Boltzmann made a variety of exneri- 
ments, all of which confirmed the theory, and showed the applica- 
bility of the above formula. 

If we make three measurements, first with the plates at distanct 
wij; secondly, at distance m^ with only air between in each case; 
and thirdly, at distance m^ with an insulating plate of thickness ft 
between, we have, if Ai, A.,, A.| be the corresponding values of A., 



_ ^-^1 



G= - 



m. 



m, 



and i = (^*^-«»h + m, + n Wn. 



The advantage of this procedure is that only differences of rn^t ^v ^t 
come in, and no absolute length has to be measured. Measure- 
ments were cdso made with condensers, in which there was no air 
between the armatures and the insulating plates; in them the 
armatures were formed by means of mercury. To give an idea of the 
agreement of the results bv different methods, we give K for 
paraffin as determined on plates of different thickness; with the 
ordinary condenser, K = 2 28, 2 '84, 2-81 for plates I., II., and 
III. ; and K = 231, 2-33 for plates I. and II. used with mercury 
annatures. 

Boltzmann convinced himself that, in the case of ebonite, Effect o! 
paraffin, sulphur, and rosin, the time during which the time, 
condenser was charged was without sensible influence. 
He found that the result was the same whether the charge 

» PhiL Trans,, 1871. 

« Pogg. Ann., cU., 1874, orSitzb. der Wiener Akad., Ixvil. 
' Pogg. Ann,, cliL 

" It is supposed that the plates are near enough to allow us Ut 
neglect the effect of Uie rims. 



38 



ELECTRIOITT 



[the DIBLSCTKia 



was inetantaneong or lasted for a cooaiderable time. The 
case was different with the imperfect insulators, gloss, 
Btearine, and gutta percha, for which he has given no 
results. To test still farther the influence of the time, 
Boltzmann measured the attraction between a sulphur and 
a metal sphere — first, when the latter was charged continu- 
ously positive or negative, and, secondly, wlien it was 
obtained positive for ^Ju*^ o^ * second, negative for the 
next T^th, and so oo ; he found the attraction to be the 
same in both cases, provided the charges without respect 
to sign were equal. This esperiment establishes beyond a 
doubt the existeuce, in the case of sulphur, of a specific di- 
electric action, wbidi is fully developed in less than j^th 
of a aecood. From experiments of this kind values of K 
were deduced, which agreed fairly well with those obtained 
by other methods. A very important result which he 
obtained was, that for a certain crystalline sphere of sul- 
phur the values of K were difierent in the directions of 
the axes, being 4-773, 3-970, and 3-811 respectively. 
The result realizes an expectation of Faraday.^ 
Scbillw Schiller employed two methods — the method of Siemens, 
"'**^ which we have already described, in which the duration of 
l^^l charge was from ^th to ^th of a second, and the method 
okHU- of electrical oscillations devised by Helmholtz. In the 
tlou. latter method K is given by the equation K = (T^ - Tg^) -^ 
(T' - T„^), where T, , T, T, are the periods of oscillation 
of a certain coil, firstly, by itself, secondly, when con- 
nected with an air-condenser, and thirdly, with the same 
condenser when the air is replaced by the insulator to be 
tested (see below, p. 82). In this method the duration of 
charge varied from jirJ^nr^ ^° Winr^ <>^ ^ second. 

The fallawing table gives some of the results of Boltzniami and 
Schiller:— 



Thomson's electrometer. The shape of the needle was also alishtlj 
different. A Goe silver vrire replnced the bifilar suspension, and the 







SchUler. 1 


Ebonite 

Panffin (clear) .... ) 
Do. (milky)... ( 

Sulphur 

Bosm 

Do, (vulcanized) 
White n^irrorgl^..' 


8'IG 
2-32 
8-S4 
2-56 


276 
I 1-92 
1 2*7 

2-34 

es4 


2 '21 
1-68 
1-81 

2-i2 
2 '89 
B-88 



The Snt column of Scbiller'e results was obtained by Siemena ■ 
method, the second by the method of oscillationi. It will be seen 
that the ibortneas of the time of charge has affected the value of K 
in the last column, reducing it considerably In all eases. BolU- 
mann's results are on the whole the latest obtained by any 
physicist ; he attributes this to the caie vith whicli he constructed 
aia plates. Gibson and Barclay found 1 97 for paraffin, and 
Siamena 2 9 for sulphur. 

Among the more recent researches on the theory of 
dielectrics may be mentioned those of Rood,^ whose results 
for crystals are interesting, and Wiillner,^ who has studied 
the course of induction when the charge is maintained for 
a considerable time. 

There are very few flnids which are sufficiently good 

iosnlators to allow an easy determination of their specific 

Slow, inductive (opacity. Meaanrements have, however, been 

^**""' mode Ijy SUow.' He used (1) Siemens'a method, and (2) 

a^ia, " "i^^*^ ^^ which he observed the deflection of a quadrant 

electrometer corresponding to the same potential, first, when 

the quadrants were filled with air, and secondly, when 

they were filled with the fluid to be examinedj the ratio of 

the latter deflection to the former la the specific inductive 

capacity of the liquid. 

The instniment actually used n-aa a ^Insa veseel, inside which 
were pasted pieces of tinfoil corresponding to the quadrants of 

■ Exp. Rii., 1689. 

' Pogg- linn., clviii., 1876. 

• Pogg. Aim., N.F. i, 1877. 

*i^. AfM., clvi.. 1S7G; clrli, 1S7«. 



replaced the bifilar suspension, ■ 
deflecUons were read off by means of a scale and telescope. 
needle and one pair of quadrants were connected with tna earth, 
and the otLer pair of quadrants charged to a constant potential by 
connection with a battery. The reacts were for oil of turpentine 
by method (1), I'468; by (2), 1-473; for a certain specinieu of 

atroleutn, by (1), 1-439; for another epecimen, by (2), 1-428; for 
mo!, by(l), 1-483. 

In the researches in which Siemens'a method was nsed, 
the spE^ed of the commutator was varied considerably, bat no 
efTect was thereby produced on the value of K, which is 
therefore, within certain limits at least, independent of the 
duration of the charge. 

Perhaps the most important of all the recent additions Q—n. 
to our knowledge in this department is due to Boltzmann,^ Bolia- 
who has succeeded in detecting and measuring the decrease '"""' 
of the specific inductive capacity of gases when rarefied. 

The principle of his method is as follows. Suppose we have an 
ordinary air-condenser inside a receiver, which we can exhaust at 
will. Let one of the armatures A of the condenser be connected with 
a batt«ry of a Urse number n of cells (Boltzmann used about 3D0 
Doniell's), while the other armature B is connected with the earth. 
If we DOW insulate B, and if the condenser does not leak, then on 
connecting II with the electrometer no deBection will be indicated. 
If, however, we increase the number of cells by one, the potential 
of A will increase from np to{n-H);j, while that of Bwili rise from 
to an amount which la proportional to p. Let the corresponding 
electrometer reading be fl. Suppose now that we altered the 
specific inductive capacity of the gas from E, to K- both amiatoies 
being insulated, A originally at potential np, and B at potential 
zero ; the potential of A wili, by the mathematical theory, hecoma 
jjl np , while that of B remair ) sero. If now we reconnect A with 
the battery of n cells, the potential of A becomes again np. If we 
then connect B with the electrometer we shall get a deQection a 
proportional to 

Let ua now ansume, what eiperiment shows to be the case, tlist 
the increase of E is very nearly proportional to the pressnre, then, 
£j and b, denoting the manometoic reading in millimetres corre- 
aponding to Ej and E, , we may write 

Here A Is a constant, the meaning of which is very simple, if ws 
assume our law of proportionality to hold up to absolute vacunm ; 
in fact, 1-1- A is in that case the specific inductive capacity* of the 
gas at 760 mm. pressure, at the temperature t of observation, and 
\ + \{l + ia) is the corresponding coefficient at 0° C. The formnla 
written above becomes therefore 

B.760 

In this way Boltzmann arrived at the following values 
for JVi at 760 mm. pressure, and temperature 0° C: — for 
air, 1-000295; carbonic acid, 1-000473; hydrogen, 
1-000132 ; carbonic oxide, 1-000345 ; nitrous oxide, 
1-000497; olefiant gas, 1-000656; marsh gaa, 1-000472. 
I'hese results are of great importance in connection with 
the electromagnetic theory of light 

Eetidual DUckarge. 
When an accumnlator, whose dielectric Is gloss or sheUac, Phwo- 
is charged ijp to a moderately high potential, and one P^, 
armature insulated, a gradual fall of the potential occnt& ^^ 
This fall is tolerably rapid at first, but it gets slower 
and slower till at last it reaches a certain limit, after 
which it remains sensibly constant for a considerable 
time. This fall is not entirely due to loss by conduction 
or convection of the ordinary kind, for we find that if 
an accumulator that has been charged to potential V, 
and has been allowed to stand till the potential has fallen 
considerably, be again charged up to potential V, then 



L 



ELECTBICITT 



39 



tlie rata of Iobb is much len tlian before, being now \ 
very nearly conatant, and not far from the limit above 
mentioned It would appear, therefore, that this constant 
limit, which on favourable dajB ia verj amall, represents 
the loas due to convection and conduction in the usual 
yte,y, and that the larger varying loss is due to some other 
cause. ^Vhen an accumolator, let us say a Leyden jar, 
has been repeatedly charged np to potential V, until the 
rate of dissipatioD has become constant, we shall say that 
it is saturated. If we discharge a saturated jer, by con- 
necting the knob for a fraction of a secoud with a good 
earth commuaication, and then insulate the knob, the outer 
coating being supposed throughout in conuectioD with the 
earth, we find that the instant after the discharge the 
potential of the knob is zero ; after a little, however, it 
begins to rise, and by and by it reaches a value which is a 
considerable fraction of V, aud has the same sign. This 
phenomenon justifies the assnmption we made as to the 
peculiar nature of the variable loss of potential experienced 
by a fresiily charged jar. The charge which reappeaia 
in this way subsequent to the instantaneous discharge is 
called the residual discharge.' If at any time during the 
appearance of the residual charge the jar be discharged, 
the potential of the knob becomes for a short time zero, 
but begins to rise again ; and this may be repeated many 
times before all trace of charge disappears. Faraday made 
a variety of ezperiments on the subject, and established 
that whenever a charge of positive electricity disappeared 
or became latent in this way, an equal negative charge 
disappeared in a similar way. He concluded that the 
cause of the phenomenon was an actual penetration of the 
two electricities (Exp. Ret., 1245) by conduction into the 
dielectric. This is not the view which is favoured by the 
best authorities of the present day ; it u indeed (see 
Manwcil, £lect. and Ma<f., vol. i. § 325) at variance with 
the received theories of conduction, and alike untenable, as 
far as we know, whether we adopt the theories of Weber, 
of Uazwell, or of Helmholtz. Faraday established that 
time was a necessary condition for the development of the 
phenomenon; and he was thus enabled to eliminate its 
influence in the experiments on the specific inductive 
capacity of sulphur, glass, and shellac. The phenomenon 
is most marked in the lost of these ; and in spermaceti, 
which relatively to these is a tolerably good conductor, the 
phenomenon is very marked, and develops very rapidly. 
>^- Kohliausch' studied the residual disharge in an ordinary 
?^. Leyden jar, in a jar whose outside and inside coatings were 
^ ~ at one time quicksilver and at auother acidulated water, and 
in a Franklin's pane, one side of which was coated with 
tinfoil in the usual way, while the other was silvered like 
a piece of looking-glass He showed, by taking measure- 
ments with an electrometer and a galvanometer, that the 
ratia of iht/ree or ditposable charge to the poletitial w coti- 
tlaiU. By the disposable charge is meant the charge 
which is instantaneously discharged when the knob of the 
jar is connected with the eartL This ratio is the capacity 
of the jar, and it appears that it is independent of the 
" residnal " or " latent" charge He showed that the 
"latent" charge is not formed by a temporary recession 
of the electricity to the uncovered glass about the neck 
and upper part of the jar ; and that it does not to any great 
extent depend on the material used to fasten the armature 
to the glass, or on the air or other foreign matter between 
them. On the other hood, his results led him to suspect 
that the " latent " charge depended on the thickness of the 
glass, being greater for thick plates than for thin. This 



' Whoowc think of the pari of lbs cha:^ that hsa disappeared, i.t,, 
ated to affMt ths potential of the knob, ve majr talk or the " latent 
iMge." This part of ths charga u aomstlmes aaiil to ba abwrbad. 

■ Pogg' 'I'M-. Kci-i 1S£1 



condusion has been questaonsd, however.' He separated 
by a graphical method the loss by Iat«nt charge from the 
loss by conduction, &c., and found ihat the aToounl of ekargt 
xdhich hteomea latent, or, which amounti to the »ame thing, 
the lou of potential owing to the forming of latent charge in 
a given time, it proportional to the initial potential ao long 
OM we operate with the tame jar. 

KohlrauBch recognized the insufGclency of Faraday's Eta 
explanation of the residual charge, and songbt to account tbMn^ 
for it by extending Faraday's own theory of the polariza' 
tion of the dielectric. The residual charge is due according 
to him to a residual polarization of the molecules of tb« 
dielectric, which sets in after the instantaneous polarization 
is complete, and which requires time for its development 
This polarization may consist in a. separation of electricity 
in the molecules of the dielectric, or in a setting towards 
a common direction of the axes of a number of previously 
polarized molecules, analogous to that which Weber 
assumes in his theory of induced mEtguetism. It is easy 
to see that such a theory will to a great extent account for 
the gradual reduction of the potential of a freshly charged 
jar, and the gradual reappearance of the residual charge. 

If the charee, and constqnently the potential, oE the jar were k?pt 
coDstaat at Qg, the residual charge tends to a limit ^od* const.) 
KohlrsDsch arannies thnt tha difference r.-iiQ, between the 
residual charge actnally formed and the limit decreases at a tat« 
which is at each instant proportional to tliis difference, and further- 
more, to a function of the time, which ho aasumes to be a simple 
power. In any actual case, where tbe jar is charged and then 
innukted, the charge varies, owing to conduction, dc, and to ths 
formation of reaidual charge, ao that the limit of r* is continually 
varying, and we muet writ« Qi for Qg, Qi denoting the charge at 
time I. The equation for residual charge is then 

i{r,-f(i,)--ht!\p(i.-t,). 



Prom tliis ba deduces the formula 



..-,(. 



Q.-QZ-iH 



t, (-*'■* 



t.a. 



which he finds to represent his results very closely, 
neatlythe same value ( -OB744, or -\ nearly) in all hia eiperi- 
mentti, p had the values 0-4289, 0'67&1, OaS82 j *ud 6 O-08B7, 
00223, O'O^ie in his thi«a cases. 

Kohlrausch called attention to the close analogy between ^ul*- 
the residual discharge and the "elastic recovery" {dattitche tf'^o* 
A'aehteirtung) of strained bodies, which had been investi- ^^ 
gated by Weber* in the case of a silk fibre, and which has 
of late excited much attention. The instantaneous strain 
which follows the application of a stress is analogous to the 
initial charge of the jar, and the gradually increasing strain 
which follows to the gradual formation of the latent or 
residual charge. The sudden return to a position near 
that of unconstrained equilibrium corresponds to the in- 
stantaneous discharge, and the slow creeping back to the 
original state of equilibrium to the slow appearance of 
the residual discharge. Another analogy may be found in 
the temporary and residual or subpermanent magnetism of 
soft iron or steeL If we wish to make the analogy still 
more complete, we have only to introduce the permanent 
polarity of tourmaline, the permanent set of certain solids 
when strained, and the permanent magnetism of hard steel. 
The phenomena of polarization famish yet another 
analogy. 

In justifying the introduction of a power of the time ■gjtgct or 
into lua equation for the residual discharge, Kohlrausch dustlDii 
makes the important remark that the time which a residual ofchorgs. 
charge of given amount takes to reappear fully may be 
different according to the way that charge is produced. 
The charge reappears more quickly when it is produced in 
a short time by an initial <Wge of high potential, than 
when produced by a charge of lower potential acting 



40 



ELECTRICITY 



[electric cub&emt. 



Max. 

weU't 
theory. 



Hopkin< 
sons 
ezperi- 
ments. 



longer. He suggests that the same thing may be trae of 
elastic recovery. He does not allade to the fact (possibly 
he was unware of it) that two residual charges of different 
sign may be superposed and reappear separately, although 
the possibility of this is to a certain extent involved in his 
remark. The analogous elastic phenomenon has recently 
been observed by F. Kohlrausch. 

Maxwell^ has shown that phenomena exactly like the 
residual discharge would be caused by conduction in a hete- 
rogeneous dielectric, each constituent of which by itself 
has not the power of producing any such phenomenon, 
so that the phenomenon in general might be due to 
" heterogeneity " simply. 

Hopkinson has lately made experiments on the residual 
discharge of glass jars. He observed the superposition of 
residual charges of opposite signs, and he suggests theories 
analogous to those of Kohlrausch and Maxwell. He finds 
that his results cannot be represented by the sum of two 
simple exponential functions of the time, and concludes, 
therefore, that heterogeneity must be an important factor 
in the cause of the phenomenon. 

The polarities of the different silicates of which the glass is 
composed rise or decay with the time at different rates, so that 
during insulation the difference of potential between the armatures 

E would be represented by a series x" \e~^' If, therefore, we 
charge a jar positively for a long time, and then negatively for a 
shorter time, the second charge wiU reverse the more rapidly changing 
polarities, while the si^n of the more sluggish will not be changed ; 
when, therefore, the jar is discharged and insulated, the nrst- 
mentioned polarities will decay more qoickly at first and liberate a 
negative charge, and, finally, as the more sluggish £dso die away, a 
positive charge will be set free. Hopkinson also made the impor- 
tant observation that agitation of the glass by tapping accelerates 
the return of the residual discharge. 

ON THE PASSAGE OF ELECTRICITY THROUGH BODIES. 

We have hitherto supposed electricity to be either 
immovably associated with perfectly non-conducting matter, 
or collected on the bounding surfaces of conducting and 
non-conducting media in such a way that the force tend- 
ing to cause it to move is balanced by an invincible resist- 
EUctric ance. We have now to consider what happens when there 
cnmnts. is a finite unbalanced resultant force at any point in a 
conducting medium. If a conducting sphere of radius a 
be charged with Q units of positive electricity, its potential 

Q ^ 

*■ this sphere by a long thin wire, 

whose capacity may be neglected, with another uncharged 
sphere of radius b, then we know that the potentials of the 
two spheres become equal; and since what we call electricity 
is subject to the law of continuity, the whole charge on the 
two spheres must be the same as before. Hence if U be 

Q 
the common potential, we must have U = — - ^ . It ap- 
pears, therefore, that the potential of a has fallen by 
•- - , and an amount — -7 Q of positive electricity 

has passed from atob, and also a --TTth part of the 

electric potential energy has disappeared. In accordance 
with our hypothesis that electricity obeys the law of con- 
tinuity like an incompressible fluid, we explain this 
transference of electricity by saying that an electric cur- 
rent has flowed through the wire from the place of higher 
to the place of lower potential. We define the intensity 
or strength C of the current as the quantity of electricity 
which crosses any section of the wire in unit of time. 

Owing to the law of continuity the current intensity is 
of course the same at every point of a linear conductor. 

^ SlocMcUy and MagneHtm, !§ 327 9iq. 



will be ~ . Connect 
a 



In the case which we have just given, the whole transference 
takes place in so short a time that we cannot study the 
phenomenon in detail. It is obvious that C will vary 
rapidly from a large initial value, when the difference 

between the potentials of the spheres is - , to zero when 

they are at equal potentials. It is possible, by replacing 
the wire by wetted string or other bad conductor, to 
prolong the duration of the phenomenon to any extent, so 
that C should vary very slowly; and we can imagine 
cases where C would remain constant for a long tim& 
Machines for producing a continuous or '' steady " current 
have been invented in considerable variety, the first of the 
kind having been the Pile of Yolta. Of such machines we 
shall have more to say when we come to discuss Electro- 
motive Force. We have seen, in the case of our spheres, 
that the passage of the electric current was accompanied 
by a loss of potential energy. The question thus arises, AppUi 
what becomes of the energy after the current dies away, *"?* *!^ 
and the equalization of potential is complete ) This leads of^ 
us to look for transformations of energy depending on the vatiaB 
electric current, or, in other words, to look for dynamical eneig) 
effects of various kinds due to it Accordingly we find the 
passage of the electric current accompanied by magnetic 
phenomena, sparks, heating of the circuit, chemical decom- 
positions, mechanical effects, kc All these are observed 
in the discharge of the Leyden jar and other electrostatic 
reservoirs of potential energy. Exactly similar effects, 
some more, others less poweiful, are observed accompany- 
ing the current of the voltaic battery and other machines 
which furnish a steady flow of electricity. In all such 
cases we have (1) a source of energy, (2) a flux of electricity, 
(3) an evolution of energy in different parts of the circuit. 
We reserve the consideration of (1) for the present, as being 
the most difficult, and devote our attention to (2) and (3). 

Ohm^s Law applied to Metallic Conductors. 

We have already seen how to measure the strength of Measv: 
an electric current in a linear conductor. According to™*°^* 
the definition we gave above, the unit current strength ^"""^ 
would be that for which a unit of electricity passes each 
section of the conductor in unit of time. If the unit of 
electricity is the electrostatic unit, this is called the electro- 
statical unit of current. We have supposed above that 
the current consists in the transfer of a certain amount of 
+ electricity in a certain direction, which we shall call tho 
positive direction of the current, and this for most purposes 
is convenient We must remember, however, that no dis- 
tinction can be drawn between the transference of -f Q 
units of electricity in one direction and the transference 
of -Q unit« in the opposite direction; for we have no 
experimental evidence on which such a distinction can be 
founded. 

We may measure the current by any one of its various Elfctn 
effects. The method most commonly used, both for indi- "^^ 
eating and measuring currents, is to employ the mag- 
netic effect According to Oersted's discovery, a magnetic 
north pole placed in the neighbourhood of a straight 
current is acted on by a force such that, if the pole were 
to continually follow the direction of the force, it would 
describe a circle round the current as an axis, the direction 
of rotation being that of the rotation of a right-handed 
cork-screw which is traversing a cork in the positive 
direction of the current. If, therefore, we have currents 
of different strength in the same wire, the force exerted 
on a magnet which always occupies the same position 
relatively to the wire will be a measure of the current. 
The force exerted on the magnet may be found by balan- 
cing it against known forces, or by allowing the magnet to 
oscillate under it and finding the time of oscillation. It 



Half's U.W.] 



ELECTRICITY 



41 



u ea^, by applying the law of continuity to multiple 
dreniU, to verify that the measurs of current iuteusity 
thus got ia proportional to the electrostatic measure. 

Thni let AB (Gg. IS) ba ■ circuit tplittiiig np into two eiactlj 
■imilu bnnches BCDO, ^ ^ 

BEFO, uid nniting W>iu 
at Q. Then, lince eleo 
tricitj behavei like in in- 
eomprcMible fluid, it a 
obTiana that any coirent 
of inteiuitj C in AB will 
iplit op into two cnmnti 
•ach of ioUniity (C ic CD 
■od EF. Bj pluiins a 
magnet in similar poaitiooi 

* Ti rtrt ^„j nn f,. ^jii t 



Fig. 18. 



ime distooce with respect to 
AB" CD, and EP, it will be EoQnil that the magnetic action id the 
lait two poaitiona ta jnat half that in the first. 

The appropriate unit in magnetic measurements of 
carrent intensity is that current which, when flowing in a 
circular arc of anit radius and unit length, exerts unit 
of force on a anit north pole placed at uie centre of the 
arc, the nnit north pole being such that it repels another 
equal north pole at anit distance with unit force. This is 
called the eUetromagneiie unit of current intensity. 
Unless thr contrary is stated, all our fonnuUe are stated 
in terms of this unit. 



L Itci 



>. To facilitate the detection and meunTement of i 
oetie meana. an instnuneot called a galvuiometer ia naed. 
■iita of a ecu of wire, of rectangnlir, elliptical, or circular section, 
inmde which if impended a magnetic needle, to as to be 
librinm Mi«llel to the coil windings under tbe mafnetic a 
the earth, or of the earth and other fixed magnets. When a 
paaae* throngh the coil a great extent of the circtlit is in thi 



If we connect two points A and B of a homogeneous 
linear condactor, ereiy point of which is at the same 
^ tempenture, by two wires of the same metal to the elec- 
. trodes of a quadrant electrometer, then, if a steady current 
C (measnred in dectrottalie unite) be flowing from A to B, 
^ we shall find that the potential at A is higher than that 
at B by a certain quantity E, which we may call the 
eleetrotnotivt force between A and B, and we may suppose 
E for the present to be measured in electrostatic unite. 
If we examine the value of the ratio ^ foe different posi- 
tions of the points AB, we shall find that it varies 
directly as the length of linear conductor between A and 
B, provided the section of the conductor is everywhere 
the same. If we try wires of different section, but of 
tbe some length and the same material, we find that p^ in 
inversely proportional to the sectional area ; in fact we 
may write 



Irl 



(1). 



«here I denotes the length of tbe wire, u its section, 
and k a constant depending on its mater^, temperature, 
and physical condition generally. This is Ohm's law. 

Ia whatever unit measured, R is called the resistance of 
the conductor. The unit of resistance can always be con- 
ceived as established by means of a certain standard wire. 
"nie unit of electromotive force is then such that if applied 
at the end of the standard wire it would generate a unit 
current in the wire. The constant k is called the tpedjic 
retittanee of the material of which the wire is made ; it is 
obviously the resistance of a wire of the material of unit 
length and unit section. 
"■ In the eleotroatatic syitem of nnitation the nnlt of E 6 the work 
1 0* done bj a unit particle of+olec(ricitj in paanng to inGnitv from 
>' tha nimce of an isolated sphere of radius unity charged with an 
atectroatatie unit of +e1ectricity. The dimeniionof Bit rQL~'1> 
wbtre [Q] It the dimtniion of tht electroatatic unit of quantity 



(see p. 2S), [q] = [l^hIt'']. Etnce the dimenaion of E is 
[l^u't'']. The nnit of C we have already disenasedi its 
dimension ia [_QT J~|_L*M*T J. From these rtsoltt, and equa- 
tion (1), it follows that the dimension of B is [l'^t], >.<., that 
of the reciprocal of a velocity. We shall show hereafter that, if C 
be measured in electromagnetic units, its dimension is[ L'M'T' J; 
hence that of Q is [l^U*], the unit of Q being the qnanti^ of 
electricity conveyed across an j section by the unit current AIsp 
EOT — work done in time T in conveying C units of + eleotricitjr 
from potential V -f E to potential T, whence [ECT] - dintenaion of 

energy -J^I^'mt"']. Hence [e]" [l*M*T~']. In this cast 
then[BJ-j_LT Ji so that in eleotromagnotic measure R has the 
dimEnsiotl of a Telocity. 

We can pnt the equation (1) into another form, which sugDeats Ohm's 
at once tha generalization oE Ohm's law for any conductor. Con- lawpoa- 
Gider two points P and Q on a liuear conductor, at a distance dx rallied, 
from each other, x being measured in tbe direction of the cutrent 
Ut the potentials at P and Q be V and V+dV, then E- -dV. 
If tt denote the current per unit of area of the section, tbenC— ua, 
and since ladme have B- — . Substituting thete values in 



(l)w 



(2), 



it ia determined at any point of a condactor by the flnx components 
uvtB, representing the quantities of electririty which in unit of 
time cross three nnit areas perpendicular to three rectangular aiet 
diswn through P. If X,Y,Z be the components of the electiic force 
at P, then the general statement of Oluu's law for a homogeDeons 
isotropic conductor is 

"-^ "-* ""t ''^ 

In such a conductor the resistance of asmalllinesr portion of ^iven 
dimensions, cut out of the substance any where or any how, will be 
the same. It is conceivable, however, that the resistance of such a 
small portion wocld be different if cut in different directions at any 
point, in which case the conductor would be eolotropic. Tbe 
most general statement of Ohm's Uw would then be 

e-j,X + r,Y+ftZ[ (*), « 

«-ftX + s.Y + r.7. 2 



inear conductors (see Maxwell, t§ 297, 324, vol. i. ], then it may be 
ibown that Uie skew system of (4) becomes symmetrical, inasmuch 

£1 — Ji. Pi~?p Pt~9r The gw*t majority of the subetances 
which the electrician has to deal are, however, isotropic; and 
Qoleaa the experiments of Wiedemann on certain crystals point to 

.1.. — I j^_^.^ — 1 . 1 .r (^jjg which has been 

nd interesting deve- 
lopmenta of t^e sobject in Haxwell, voL i. 1 297 ijg. 



(colotropic conduction, we do not know of any ci 
experimentally examined. The reader will fine 
lopmenta of the sobject in Haxwell, voL i. 1 297 

A very important remark to he made with n ^ 
tiona (4) ia that, being linear, the principle of saperposition 
applies. "Thaa, if u,v,v! be the current components due to electric 
forces X,Y, Z and u\tf,vf similar components fotX',Y',Z', then the 
curTentforX + X',Y + Y'. Z + r is givenby u + u", e+e-, « + »". It 
ia obvioos, moreover, that (4) are the most aeneral equations that 
can Im written down to connect carrent with electromotive force, 
subject to the condition that the currents due to snperpoted elec- 
tric forces are to be found by the superposition of the canents due 
to the separate forces. 

Betides the equations (4), u,v,u are subject Uke any other flux 
componenta to an equation of continuity. This equation, invet'ti- 
gated in the usual manner, is 

ifu ife Aff rfp _n .£> 

tbe di/ dt dt 

where f is the electric Tolnme denntv at the time t At a mrfsce 
of discontinuity (6) must he replaced by 

(u-u')I+(ir-«')n + (ir-w')«-2f-(' • ■ («)- 

where «,»,«, and i^y,^ are componenta of floi on the firrt at>d 
second sides of the snrfaoe, l,m,n the direction cosines of the nonnsl 
VIU. — 6 



42 



ELECTRICITY 



[klkctbic CUSi 



drawn from the Gnt to tlie Mootid dd^ and a Qie electric iiufue 
denBit; at time (. 

If we cooaiJer the particnkr caw of homogeaeooi uotropJc 
media, and «up|)ose further that X=- jT'^=-~j'' 2 = - jT' 
thew tquatioiis redace to 

d'V_^d'Y_^<PV_> ... 

a3"^5?*i?-*i( '''• 

, l^x ] dV,_<fa ... 

■"^ -k,-d^^i^lf'^ <^'- 

In the last eqnttioa V, and V, are the potentials on tlie two sides 
of ■ boundary lietweeii media of sjiecifi'' resistance k^ and J;,. 

In the particular esse of ateadj motion, the right-hand aides of 
(7) and (8) are zero. The analytical treatment ol proiiUms about 
steady currents is thercfoie yrecisely analogous to tliat of proLlcms 



, fee: 



y so\i 



such physical subjcc 
rs. Many valuable di 
found in Thomson's papers on clectrosUtia 



tills subject 
and magneti 

I The cousequences of Ohm's law have been followed 

'■ out mathematicaU}', and verified in a variety of cases. 
We shall notice a few which are intereating, either from 
the accuracy of the experimental results, or from tlie 
interest or practical importance of some method or prin- 
ciple involved. 

i- In the case of a steady current in a uniform linear con- 
ductor, say a wire, it is obvious that the potential must 

' fall nnifonnly in the direction in which the current is 
flovriDg. Hence, if we suppose the wire stretched out 
straight, and erect at different points lines perpendicular 
to it, representing the potential at each point, the locus of 
the eztiemities of these lines will be a straight line. 

This may be arrived at by intt^ntting equation (5), which be- 
comes in this case j^ = 0, x being measured along the wire sup- 

mstant I from the origin, at w 



If T be taken as ordinate, this represents a stnught line, the 
tangent of whose inclination to the x-azis is , or ~ Kit. 

Tolialc We cannot apply Ohm's law at the junction of two 
EucuiL different aubatancea. The condition of continuity of 
course applies ; in other words, if the flow has become 
steady, the current is the same at all poiats of the circuit, 
whether homogeneous or not We shall see, when we 
come to discuss electromotive force, that there is a con- 
stant difference between the potentials at two points in- 
finitely near each other, but on opposite sides of the 
boun»kry between two conductors of different material 
If we knew this potential difference for each point of 
heterogeneous contact in the circuit, wo could draw the 
complete potential curve for the circuit by applying Ohm's 
hw to each conductor separately. The diagram (fig. 19) 
represents (on the con- 
tact theory, as held 
by Ohm, see Origin of 
Electromotive Force) 
the fall of potentials 
and the discontinuities 
in a voltaic circuit, ^- ^'- 

consisting of zinc, water, and copper, in which the current 
flows from Cu to Zn across the junction of the metals. We 
assume for the present that Ohm's law applies to the liquid 
conductor. 

Let us denote by V^ y%, Ac the potentials at Q and R, 
tui,, or what is the same thing, the ordinatcs BQ, Bit, &c., 
in onr diagram. Then applying Ohm's law to the homo- 
geneous parts of the circuit, we have Vt — Vq ~ CR', 
V, - V, - C&, V, - Vd - CU", where B', S, E", denote the 



-fi-A 



resistances of the zinc, the vater, and the copper respee- 
tively. Now, denoting Vy-Vo, the potential differancA, 
or as it is sometimes called, the " contact force " between 
Zn and Cu by £ic and so on, let us add the above three 
equations ; we thus get 

E=:EK+EM-*-Ec4-C(R'-hE"-fS). 
Here E is called the v>}iole eledromuive fonx of the circuit, 
being the sum of all the discontinuities of potential, 
taken with their proper signs, or, what is equivalent to the 
same thing, the whole amount of work which would 
be done by a unit of + electricity, in passing round the 
whole circuit once, supposing it to get over the discon- 
tinuities without gain or loss of work. Defining E in this 
way, we may extend Ohm's law to a heterogeneous circuit, 
the resistance R being now the sum of all the resistancea 
of the different parts, or the whole resistance. In accordance 
with this definition, if we take two points, p and { (fig. 
1 9) in the Cu and Zn respectively, the whole electromotive 
force will be V, - V, -i- £„ and the current will be given by 

V,-V,-(-Eic-EC (10), 

where B is the whole resistance of pq. V, - V. is somo- 
tiiues called the " external," and Eic the " internal " electro- 
motive force. If p, q include more than one contact of 
heterogeneous metals, we have only to add on the left- 
band side of (10) the corresponding internal electromotive 
force for each discontinuity. 

If p end n be connected by wires of the same metal, 
say copper, to the electrodes of a Thomson's electrometer, 
then the electrometer will indicate a potential difference, 
V,-V, + E„;, and notV,-V, as might st first sight be 
suspected.^ No electricity can flow through the electro- 
meter, hence the copper wire attached at p, and the pair of 
quadrants to which it leads (we may suppose the quadrants 
made of copper, but in reality it does not matter, see beloir. 
Origin of Electromotive Force), will be at potential V^ But 
owing to the contact force between the Zn and Cu at q, the 
wire from q and the quadrant to which it leads will be ftt 
potential V, - Ek- It appears, therefore, that the electro- 
meter indication corresponds to the vshiAe electromotive 
force between p and q, and is proportional to the whole 
resistance between p and q, uo matter what metals the 
circuit may include.' This conclusion was verified by 
Kohlrausch, His method rested on the principle of Volta'e 
condensing electroscope. 

He used an accumulator consisting of a filed plate B, and an V«ll 
equal movable plate A, which could be lowered to a very snudl titn I 
fixed distance from B, and raised to a coQStderable distance, *o as %iM 
to touch a filed wire leading to a Dellmann's electrometer. The laoK 
plate A waa lowered and connected witb Ji, while ^ and the fixed 
plate were connected with the ground; the connection withy was 
then removed, and A raised, its potential thereby greatly increaana 
owing to its greatly diminished capacity. This increased potrntiJ 
was mettfluri'd liy the electrometer, vrilb wliich A was in connection 
through the fixed wire. In one of Koblrausch's eiiieriments, be 
found for the electromotive force between a fixed point of the 
metallic circuit and four points, such that the resiEtance between 
each ac^'aceut p^r was very nearly equal, the values O'SS. I'Sl, 
2-69, 370; the values calculated by Ohm's law were 0-D3, ]-86, 
280, 373. He also examined the fluid part of the circuit, and 
still found a good agreement between theory and iiperiment. (See 
Wiedemann, % 102.) 

The laws of current distribution in a network of linear N«t» 
circuits were first studied by Kirchhofl'. He laid down ™^ 
two general ]>rinci])les which are very convenient in prac- ^^^ 
tical calculations. 

I The algebraical sum of all the currents flowing from 
any node of the network is zero. 

XL If we go round any circuit of the network, then no 



It Is inppoBBd that alt the wires sre at the same tempeimtnn. 
This more general statement follows it ones bom Um •bOT* 
TcasoDlng in conjunction with Volta's law {pf, below, Oiigin of ElM- 

- ■" Foroet, 



OHll'S LAW.] 



ELECTRICITY 



43 



matter how many meshes it may include, or what con- 
ductors may branch off at different parts, we have 

where E is the tohde iiUemal electromotive force, and R^, 
Rj . . • . C^, C2 . . > are the resistances and current strengths 
in the different parts of the circuit 

The first of these principles is simply the law of con- 
tinuity, and the second is got at once by applying 
equation (10). 

We ffive here an inyestigation of the cnrrents and potentials in a 
netm'ork of conductors. The method and notation are taken from 
Maxwell, voL i. § 280. Let A], A^ ... An be n points, con- 
nected by a network of in(n-l) conductors (that being the 
number of different pairs of conductors that can be selected from 
the n). Let C^, £^, K,^ denote the current strength, internal 
electromotive force, and conductivity , 1.0., the reciprocal of the 
retistance, for the conductor Ap A^. Let, moreover, the potential 
at Ap be P^ and the current of electricity which enters the 
•y>tem there be Q^ It is obvious from our definitions of the 
■ymlx^ that 

K^=Epf, C^=-C^ £pf=-£^, 

and, by the condition of continuity, that 

Qi + Q,+ +Qn=0. 

At the point A^ we have 



Now 



CVi + C„ + 



+ CV«=Q, 



Cpg = Kp,(Pp-Pj+Ep,) .... 

Hence (a) becomes 

K,i(Pi - Pp) + Kp.(P, - Pp) + + Kpn(P„ - P,) 

The symbol K^ does not occur in this equation, and has no mean- 
ing as yet. Let us define it to mean - (Kpi + K^j .... Kpn), where 
K^ does not occur. Then we have 



(a). 
(7). 



+ K«. = 0, 



(») 



K,i + Kps + . . . + K + . . 
and, multiplying by P^ - P^ , 

K,i(Pp-P,) + . . . + K„{V^-Vr) . . . Kp»(P^-Pr) = 0. 
Adding this last equation to (7) we get 

K,i(Pi-Pr) + K„(P,-P.) + . . . + Kp„(P«-P.) 

= KpiEpi + . . . +Kp«EpH-Qji . . (c). 

In this Muation the term whose coefficient is K^r of course 
vanishes. By giving p all possible vidues except r, we get a sot of 
n - 1 equations to determine the n - 1 quantities Pi - Pr , P, - Pr , 
Itc Hence if Mrr denote the minor of Krr in tne detenuinaut 
A = (K|jK., .... Kwi) ;^ and if Mr»y denote the minor of IL,, 
in Mn^ we nave 

(Pp-P,.)Mrr-|KiiEii + Ki,Ei,+ . . . +KinEi,-Qi|Mrrlji 

+ {K,iE,i + K,,E„ + ,-Q}Mr,2p 

+ &c (0, 

where of course Eij and £,, are zero, and ^Irrrf docs not occur. 

This expr^on is Unear in the letters £ and Q, and the principle of 

superposition holds, as we saw it ought to do in all applications 

of Ohm's law. 

Consider the mrticular case in which all the Qs and £s vanish, 

excei>t £|« and Emj ( = - Eim), we then have tlie case of a linear 

circuit in which an electromotive force £<• is introduced into 

AjA^ . We get from (f ) 



and 



Henct 



and 






,). 



). 



C„=?«S^-(M. 



P+Mrr.^), 



Similarly, if Cte bo the cuiTcnt in AiA* due to an electro- 
IDOtive force £^ in A^, , we get 



~fi^ <^'^ - ^"1« - M-tl + ^"f) 



w. 



^ This detanninant has many properties of interest to the mathe- 
matical student; «.y., in our notation Mn = M,, . . . = Mmi» 



Now, since A is a sjrmmetrical determinant, Mrv^ = VLrnt » &c., 
and the expressions within brackets in (1}) and (0) are idtenticaL 
Henc^ foUowB the important proposition : — 

If an electromotive force equal to unity, acting in any 
conductor A|A» of a linear system, cause a current C to 
flow in the conductor A^A^ then an electromotive force 
equal to unity, acting in A,,A^, will cause an equal 
current C to flow in A,A .. 

If we suppose all the conductors of the system except A|A« and 
A^Af removed, and A|A^ and A^A^ joined by two wires, in such 
a way that for electromotive force imity in A|A» the current in 
A^Af is C then the conductivity of the circuit which we have thus 
constructed would be 

-^^ (Mn^rf - Mrryw - Mrrgl + Mrrt«) i 

this might be called the reduced conductivity of the system with 
respect to ApA^ and AiAm. When the expression within brackets 
vanishes, the conductors A.A^ and A{A« are said to be conjugate. Coi^Ja- 
The reduced resistance in tnis case is infinite, and no electromotive gate con- 
force in AfA«, however great, will produce any current in A^A^, ductozs. 
and reciprocally. 

Similarlv, we may prove that if unit current enter a h'near system 
at Ai and leave it at A*, the difference of potential thereby caused 
between Ap and A^ is the some as that caused between A| and A*, 
when unit current enters at A, and leaves at A4. (See Maxwell. ) 

The case of several wires forming a multiple arc very Multiple 
often occurs in practice. p. atc 

Let AB, CD (fig. 20) 

be two parts of a circuit -i-J5^>5^ ,^ ^<^ :>S "d 

whose resistances are R 
and S, and let the cir- 
cuit branch out between ^8- ^^' 
B and C into three branches of resistances R^ , R^ , B3 • 

We have Vb - Vc = KjCi = K,C, = RjC, , and 

1 




Ci = 



A 



C 



Also 



1 + 1 + 1 



C, = &c. 



Va- Vd = Va- Vb + Vb- Vc + Vc- 



(R + p + S)C, 



whe' 



1.1 + 1 + 1 



Hence current in each branch is inversely propor- 
tional to the resistance, that is directly proportional to the 
conductivity; and the reduced conductivity of the multiple 
arc is equal to the sum of the conductivities of its branches. 
These statements are obviously true for any number of 
branches. 

Some of the most important applications of the theory B^^yt. 
of linear circuits occur in the methods for comparing ance 
resistances. The earliest method for doing this consisted measurt 
simply in putting the two conductors, whose resistance it ^^^ 
was required to compare, into a circuit which remained 
otherwise invariable ; if the current, as measured by a 
galvanometer, was the same, whichever conductor was in 
the gap, it was concluded that their resistances were equal. 
The difficulty in this method is that the electromotive force 
and internal resistance of the battery are supposed to 
remain constant, a condition which it is excessively hard 
to fulfil 

This difficulty can be avoided by using a differential 
galvanometer, or the arrangement of conductors called 
Wheatstone's bridge. The differential galvanometer differs Diiferoa- 
from an ordinary one simply in having two wires wound tial gal- 
side by side instead of a single wire. If .we pass equal ^JJJ^^ 
currents in opposite directions through the two wires, the 
action on the needle is zero, provided the instrument be 
perfectly constructed. If the currents are unequal, the 
indication will be proportional* to the difference of the 
current strength. 

If the coils are not perfectly symmetrical, but such that 



44 



ELECTRICITY 



[albct&ic cu&bkmt. 



the deflection^ due to a current c in one is mc^ and in the 
other nc^ where m and n are the '' constants'' of the two 
coils, then the deflection for currents c^ and Cj is tuc^ - nc^ 
Fig. 21 gives a scheme of the arrangement for measuring 
resistances with 
this instrument V 
is the battery in- 
serted in the com- 
mon branch ED of 
the two circuits, 
which convey cur- 
rents dividing off 
at D, and going 
in opposite direc- 
tions round the 
coils of G. If 




Fig. 21. 
we wish to measure the resistance of a 



wire, it is inserted at AB by means of binding screws or 

mercury cups, and the resistance of the other circuit is 

varied until there is no deflection ; then AB is replaced 

by a known resistance, which is made up until there is 

zero deflection as before. 

It is obvious that the only requisite here is that the 

resistances of EFK, EA, BL, and the galvanometer coils 

should remain constant. Variations in the electromotive 

force or internal resistance of the battery do not affect the 

result. 

The method which we have thus sketched is the best way of 
using the differential galvanometer, and it does not matter even if 
the coils are not exactly symmetrical. Let the constants of the 
coils M and N be m and n, so that the deflection due to currents 
Ci and c, in M and N is ^<;i *- n<;, . Let the resistance from E to 
D in the single branch be B, and in the circuits £FE and EABL, 
which pass round M and N respectively, R and S + U , U being 
the resistance between A and B , which is such that the deflection 
is zero. Then 



0- wujj-wc, - j wi(S + U)-nR |g . . . 



(a). 



where £ is the electromotive force of the battery, and 

L> - (R + S + U)B + R(S -f U) . 

Suppose we substitute U' for U, and arrange U' so that we have 
again zero deflection. Then 



0- |w(S+UO-nR|g, (/8). 



From a and /3 we get (J— U'. 

For farther details concerning this method, see Maxwell, vol. i. 
§ 846, and Schwendlcr, PhU, MOg., 1867. 

The differential galvanometer method was much used by 
Becquerel and others, but it is now entirely superseded as 

Wheat- * practical method in this country by the Wheatstone's 

•tone's bridge method. Suppose we 

Wdge. have a circuit ABDC of four 
conductors. Insert a galvano- 
meter G between B and C, and 
a battery between A and D. 
Adjust say the resistance AB 
until the galvanometer ia BC 
indicates no current. The bridge 
is then said to be balanced, and 
the potentials at B and C must 
be equal. But the whole fall of potential from A to D 
along ABD is the same as that along ACD ; hence if the 
fall from A to B is to be equal to that from A to C, we 
must have 

R T 
S"U' 

where R,S,T,U are the resistances in AB, BD, CA, DC. This 
is the condition that BC and AD be conjugate. We might 
have deduced it as a particular case of the general theory 
given above. Hence if we know the resistances S,T,U, we 




Fig. 22. 



^ The deflections are supposed small. 



max 

OBQI 



ST 
get in terms of these R « Yf- ^ ^ often called the standard 

resistance, and T, U the arms of the bridge or balance. 
The sensibility of this arrangement may be found practi- 
cally by increasing or decreasing B so as to derange the 
balance. The largest increase which we can introduce 
without producing an observable galvanometer deflexion 
measures the sensibility of the bridge. 

If we had a given set of four conductors, and a batteiy An 
and galvanometer of given resistance, then it may be 
shown (see Maxwell, vol. i. § 348) that the best arrange- _ 
ment is that in which the battery or galvanometer connects ab^ 
the junction of the two greatest resistances with that of 
the two least, according as the former or the latter has 
the greater resistance. The practical problem might take 
another form. We might have given a resistance, and have 
at our disposal known resistances of any desired magnitude 
to form our bridge. We might also suppose further that 
we had given the total area of the plates of our battery, 
and the dimensions of the channel in which the galvano- 
meter wire was to be wound. We may neglect the thick- 
ness of the silk coating, or assume that it is proportional 
to the thickness of the wire. 

Then, B and G being the resistances of the battery and galvano- 
meter, the electromotive force £ a VB, and the number of tarns Id 

the galvanometer ocVq. 

L^t us put S— ^R, T— 2R, and IJ»2^2R. These resistances 
would balance ; let us however put (1 +ir)R in the branch AB in« 
stead of R, the others bein^ unchanged, and calculate the effect on 
the galvanometer in 6, which we put proportional to the current 
in B(y, and to the number of turns on galvanometer. Then, from 
equation (ly) (or Maxwell, vol. i. 349), we find that the deflection f 
varies as 

y2\^BG . 

(1 + y)(l + 2)BG + y(l + 2)«BR + 2(1 + 2/)«GR + y2( 1 + y}(l + a)R« • 

in order that Z may be a maximum, we must have 

G{(l + y)(l+2)B+2(l + i/)«R}-y(l+2)»BR + y2(l + i/Xl+2)R* UV 

B{(l + y)(l+2)G + Ml+«)'R}-2<l + i/)»GR+yr(l+j/Xl+2)R* (3X 

BG-2R« . . . . {y\ 
BG=t/R« . . . (dX 

a and /3 give at once by addition and subtraction 



or 



B-2 



1+2 



G-yJ±iR 
1 + y 



(tX 
(ft 



Ck)mbining the four equations (7), (5), (t), (f)» we get 
y = 2-landB-a-R-S-T-U. 

It appears, therefore, that when all the resistances on 
the bridge are at our disposal, we ought to make them all 
equal to the resistance to be measured, or come as near 
tlus as we can ; e,g,y if we had a very small resistance to 
measure, we should make the arms of the bridge small, and 
take a small-resistance in preference to a high-resistance 
galvanometer. 

In order to carry out measurements of resistance with stas 
ease we must possess a series of graduated resistances, with ^ 
which we can compare any unknown resistance, and of'^'"' 
which we can make the arms of our balance, d^c. Again, 
if the measurements of one electrician are to be of any use 
to another, there must be a common standard. It would 
be most convenient to have only one standard for all 
nations, and this standard might be either arbitraiy, like 
the standard of length, or absolute in some sense such as we 
have defined above. Arbitrary standards have at different 
times been proposed by Jacobi and others. The mercury 
standard of Siemens, to which we alluded in the historical 
sketch, has obtained great prevalence on the Continent. 
The British Association unit or ohm is an absolute unit. 



ELECTRICITY 



45 



inasmuch aa it profeases to represent in electromagnetic 
meaaure a velocity of 10" centimetrea per aecand, or, 
taking the original definition of a metre, an earth quadrant 
per second. It happens, by a curious accident, that the 
mercury unit and the ohm are very nearly equal, the 
latter being eipreased in terms of the former (according to 
Dehma and Hennann Siemens ; see Wiedemann, Bd. it 2, 
j 1074) by the number 10493. 

One of the earliest iDstrumeota for furnishinga graduated 
resistaoce waa the rheostat, bronght into use by Wheat- 
stone, but also invented independently by Jacobs at St 
Petersburg about 1S40. 

It coiuUted of two cyliDdvn of equal diameter, one of wood and 
one of brua. A wire, whose extremities were in coDnectioD with 
the metallic uea of tbe cylinders, wu wound in opposite directioiu 
round the cyliudets. The *ies of tbe cylinders were cotuiected 
with two bindins scrawe by means of ■lidlng contacts. The part 
of tbe wire which does tut lie on the metalcylinder ia the only 
part that produces resistance between the binding screws ; and, by 
winding and unwinding, we can increase or diminish the resistance 
coDtinuouily to a known extent, means being proTlded for measuring 
the angular rotation of tbe metal cylinder. 

We shall not stop to consider the defects of this instrU' 
ment, which is now never used for delicate work. Its 
place is taken by reaistaoce boxes, containing coils of 
wire whose resistances are different multiples of the nnit 
of resistance (in this country always tbe ohm). The 
reader will find a full account of the methods by which 
the atandards are reproduced in the collected reports of 
the Committee on Electrical Standards. The usual material 
for tbe wire of resistance coils is Qerman silver. Most of 
tbe copies of the ohm issued by the British Association 
were made of an alloy of two parts of silver to one of 
platinum. The great advantage of alloys is that the varia- 
tion of resistance with temperature is smalt for them; in tbe 
FtAg alloy, for instance, it is less than a tenth of tbe value 
fur an average pure metaL To secure insulation the wires 
are carefully coated with silk, and after winding the coil 
is immersed iu melted paraffin. To get rid of electro- 
magnetic and inductive effects, the wire on resiatance-coik 
is doubled on itself before being wound, so that, when a 
current passes tbrongb tbe coii, there are always two equal 
and opposite currents at each point. Tbe terminals are 
formed by stout piecea of copper rod, whose resistance ia 
either included in the coil, or is so small that it may be 
neglected. The connections fur smalt resistances are 
managed by means of mercury cups, with pieces of 
amalgamated copper at the bottom, on which the copper 
electrodee are made to press. 

For ordiaaiy imrposes the coils are arrenged in > box (fig. 23), 
the tsrminals being stont pieces of brass fixed on the ebonite Ud ; 




ng.23. 



o throw tbs 



eoolcal brass pings inserted between these pieces serv 
GoiJs in and out of circniL The box represented ui uj, ^a u> 
specially amiued for use la Wheatstone's bridge. In ^F,0 wo 
have a setisi oT coils, lOOO, 100, 10, 10, 100, lOOO ; thcM are used 
for the artnt of the bridge. In A,C,D there are sixteen coils,], 2, S, 6, 
10, 20, SO, H, kc, which gire us an; rMiitance of a whole number 
of ohms fron 1 np to 10,000. In actual use the resistance to be 
maasQied ia inserted between A and O, D and V. an connected br 
a stout pisM d oopper, tbe galvanometei is inserted between F and 



A, and the battery twtween E and 0. The naialances of the arms 
of the bridge are taken equal, and as near the resistance to be 
measured as possible. In this way the resistance of any conductor 
may be very quickly found to an ohm. If it is deaired to go 
fartlier, we may proceed thus. Snppoee that we have found that a 
reaistanee lies between E and S, put in the arm FE 100, and in 
FO 10, let the resistance in DCA, when there is a balance, be 67, 
tbenthe resistance ofthe conductor is i>A xS7, or57. Similarlywe 
mi|;ht go to a second place of decimals by putting 1000 in FE and 
10 in FQ. There is a limit, however, to this process, because the 
increase in the resistance of the arm decreases the " sensibility'' of 
the bridge. Another method is to balance aa nearly as possible, 
and then interpolate by taking the deflection of the galvanometer. 
Suppose, for instance, in the above case, that, with G ohms iu 
DCA, the deflection was 21 in one direction, and, with 6 ohms, 9 
in the other direction, then, taking the deflection proportional to 
the deviation from balance (see formula for 3 above), we have 



We might also coostmct small graduated resistances ; Condno- 
and this would enable us to use smaller arms in the bridge, ^'"V 
and thus increase the "sensibility" when used to measure^'"" . 
small resistances. Owing to the multiplication of con- ^c. 
nections, there is a limit to the ordinary reBistance boic 
arrangement. The difficulty may be evfided to a certain 
eitcnt by using conductivity boxes, according to Sir W. 
Thomson's suggestion, where the resistances are arranged 
abreast, so that a small alteration of tbe resistance is 
brought about by adding on a vert/ greai resistance to the 
multiple arc. "The rheostat principle has been used by 
Poggeudorff in hia rheocord for producing small resist- 
ances. He stretches two platinum wires side by ude; on 
these is strung a hoUow box filled with mercury, wLose 
longitudinal motion is read off on a scale. If this arrange- 
ment be thrown into any circuit by means of two binding 
screws connected with adjacent terminals of the wires, the 
parts of the two wires up to the bridge give a small resist- 
ance, which may be adjusted at pleasure. 

In tbe quicksilver agometer of MiiUcr (Wiedemann, L 
§ 160), the resistance is formed by a column of mercury 
of variable IcngtL We may remark here that difficulties 
equally arise in constructing very large resistances. To 
get such within reasonable compass the wire must be ex- 
ceedingly thin and the insulation very good. Messrs 
Warden and Muirhead have wound coils of fine wire, 
giving a resistance of 100,000, and have conatructed iu 
compact form resistance boxes np to 1,000,000, or a 
megohm, and beyond. They have also given practical 
form to a suggeation of Phillips ta utilize the resistance of 
carbon, by drawing fine pencil linea on ebonite or glass ; 
they mix plumbago with the pulp in the ordinary procesa 
of paper manufacture, and thus produce a species of carbon 
paper, A atrip of this about 21 in. long and '5 in. broad 
gives a resistance of about 60,000. Thia seems a valuable 
invention; but we are not aware how far it has stood the 
test of practical use. 

Selenium and telloriam have been proposed as material 
for high resistances, but owing to the variability of their 
resistance under the action of light, &c., they are unfit fur 
the purpose. 

The best method for compaiing resistances with great Kireh- 




Fig-Jt 

accuracy is the modification of Wheatstone's bridge intro- 
duced by Kirchhoff (fig. 24). 



46 



ELECTRICITY 



[klscikio cubsikt. 



KL is a platinnm-iridinm wire, DK and HL are stout copper 
terminals to which it is soldered, DAE, EGF, FBH are stout 
copper pieces with binding screws and terminals for mercury cups, 
by means of which resistances R,T,U,S can be inserted at D,E,F,H. 
A, B, and G are binding screws for the battery wires and one 
end of the galvanometer wire. The other end of the galvanometer 
wire is screw^ to a sprint contact piece fixed to a sliding block 
at P ; when the button of this block is depressed, contact is made 
with KL, at a spot which is definite to an eighth or tenth of a 
millimetre. Platinum iridium is chosen for Kl^ because it is 
hard and tough, not liable to be scratched or abraded by the con- 
tact piece, does not oxidize or amalgamate with mercury, and 
changes very slightly in resistance when the temperature alters. 
The wire must be calibrated to find what correction, if any, must 
be applied for variation of resistance per unit of length at different 
parts ; for methods of doing this see Miitthicssen and Hockin ; Brit, 
Assoc, Beports on MectriccU Standards, p. 117 ; or Foster, Joum, of 
Society of Ttlegraphic Engineers, 1874. 

Foster's Kirchhoff*8 arrangement may be used in the ordinary 
method, way after we have made special experiments to determine 
the resistance of the connections, <S^c. Professor Foster 
(/.c.) has given a very useful method, by which the differ- 
ence of two resistances can be got independently of the 
resistances of the connections. Suppose we wish to find 
the difference between B and S, which we suppose so near 
each other that, with the arms T and U approximately 
equal, there will be a balance when P is somewhere on 
KL. Let the reading for the position of the block be x, 
taken from left to right. Interchange R and S, balance 
again, and let the new reading be of (we suppose the 
difference between R and S so small that P is still on RL); 
then, if /A be the resistance of unit length of KL, H - S 

= fl{Qlf - x). 

For, if a represent the resistance of the connections in DE, 
the same for the other end of the wire, and if T and U indude the 
resistance of the invariable connections, then we have 

U+a + ux _T 

where 2= length of KL. Hence 

R + g + fUg _ T 
R+S-j-o+jS + AtZ fTU' 



Similarly 



therefore 



R-S-^(ar'-ar). 



Methods 
of Mat- 
thiessen 
and Hoc- 
kin and 
ofSirW. 
Thom- 
son. 



If we have to find the resistance of a thick cylindrical 
body, what is really wanted is the ratio of the current 
strength to the difference of potential between the two 
ends, when the current flows parallel to the axis at every 
point. The last condition is not generally fulfilled. It is 
obviously not so in the case where the cylinder is joined 
up with a thin wire. In cases where we wish to compare 
the specific resistance of two metals which we possess in 
cylindrical pieces, we get over the difficulty by observing 
the potential at a point at some distance from the end of 
the piece, where the flux is parallel to the axis at all points 
of the section. 

Matthiessen and Hockin used the following method for this pur- 
pose (fig. 25). The two pieces XZ, YZ are soldered together and con- 
nected in circuit with 

two resistance coils A f ~ — 7^' 

and C, and a graduated I f _ ^^ ' T • T' 

wire PR as before. J Ti ' > ■ = r~ > -^^^^ ^ jx 





S, S' are two sharp 

edges, at a measured 

distance apart, fixed 

in a piece of ebonite 

or "hard dry wood, - 

and connected with ^^^' **'• 

mercury cups. T, T' is a similar arrangement for YZ. The 

galvanometer is inserted between S and Q, and the position of Q is 

found for balance; then the terminal is shifted to S', and if 

necessary the resistances A and C altered, so as to keep Uieir sum 

constanL until balance is again found. The tame is done for 

T and T. Then, XS denoting the resistance between X and S, and 

A,9 Ci th« valoet of A and C m the fiist case, and to on, we have 



where 
Hence 



Similarly 



Therefore 



XS Ai + PQi XS'_Aj+PQ, 
XY" K 'XY" R • 

R=Ai+Ci-l-PR=A,+C,+PR 

SS;_A^-A, + QiQ, 
XY" R 

Tr_ A,>A,+Q,Q^ 
XY" R 



SS'^A^-A^+QjQ, 
TT"A,-A,-hQ,Q4' 



This gives us the ratio of the resistances between SS' and TT. 
The nlethod does not depend for its success on the goodness of the 
contacts at SS', &c. Another ingenious arrangement for effectins a 
similar purpose is due to Thomson, and wifl be found described 
in Maxwell, voL i. § 351. * 

In measuring very large resistances, such as the insular Bcsi 
tion resistance of a telegraph cable, it is convenient to use 

the quadrant electrometer. One end of the cable is con- 

nected with one electrode of a condenser, the other end will 
of the cable is insulated, and the other electrode of else 
the condenser put to earth. The condenser is charged,"** 
and the difference of potential between its electrodes 
measured by means of the electrometer. If E^, E, be the 
value of the difference at the beginning and end of an 
interval of t seconds, and if S be the capacity of the 
condenser in electromagnetic measure, then the reebtance 
of the cable is 

t 

S(log.Ei - log,EJ 

in electromagnetic measure. If the condenser itself leaks^ 
we must determine its resistance by insulating the 
electrodes and operating as before. Then, regarding the 
circuit in the first experiment as a multiple arc, composed 
of the insulation of cable and the dielectric of condenser, the 
true conductivity of the cable envelope is the difference of 
the conductivities obtained in the two cases. Several other 
methods might be used to compare metallic resisistance 
but they are of small importance compared with those we 
have now been describing. 

The reader who desires information concerning the ap- 
plication of Ohm's law to conductors other than linear 
will find the sources sufficiently indicated in Wiedemann'is 
Galvanismxis; some of them have been alluded to in the 
Historical Sketch. 

Application of OhnCs Law to Electrolytes. 

In our discussion of Ohm's law, we have hidierto had 
in view principally the metallic part of the voltaic circnit 
We now turn our attention more particularly to the fluid 
parts. It is of no importance in the present connection 
whether the fluid forms part of the " battery " or " elec- 
tromotor," or whether it is inserted outside the battery ; 
the only difference in these two cases is, as we shall here- 
after see, that in the former case energy is being absorbed 
by the current, and in the latter it is being evolved. In 
many respects the properties of the metallic and fluid parts 
of the circuit are alike : the electromagnetic action is the 
same for both ; heat is also developed in the body of the 
conductor, whether metallic or fluid, according to the same 
law. But there is one peculiarity about a large class of Bk 
fluids which has no analogue in purely metallic conduction, ^ 
viz., that^in them the passage of a steady current of elec- 
tricity is invariably accompanied by chemical decomposi- 
tion, definite in kmd and quantity. To such fluid 8nb> 
stances Faraday gave the name of electrolytes. 

For example, suppose we fill a small beaker with a solution oC 
zinc chloride (ZnCl^, and suspend in the liquid two strips of jJ^ 
tinum foil (caUed electrodes), at a moderate distance apart Lai 
a current enter at one of these strips, which we shall call the anode^ 
and leave at the other, i^iioh we shall call tha cathodeu It will be 



ELECTRICITY 



47 



anadl^ The metallic aac precipitates, and the chlorine combinei 
with the pUtinnm of the uioda to form platioic chloride. 

It U obvioual^r eeaeatial in an electrolyte that it slionld 
be a compound in some sense or other. It is not, however, 
true that ail compound bodies are electrolytes. Fluidity 
is also a necessary condition, whether attained by heating 
to the melting-point, or by dissolving in water or other 
solvent. Faraday established as a law, to which there ap- 
pear to be few, if indeed any, exceptions, ^-(A^ all sub- 
ttaafxt uhiek in the tolid tlate are very bad condudon, but 
etmdud on bring heated (o the meltitiff-point, are eUctrolytes, 
Le., are deeompoud by the patsagc of the electric curreat. 
Faraday thnught that periodide of mercury, Buoride of 
lead, and some other bodies were exceptions to this law ; 
but later researches seem to have established that this is 
not BO. (Cr. Experimental Rttearehet, 4U, 439, 1340, 
Ac, and Wiedemann's Galvaaitmus, L $ 191, iic.) The 
conductivity of eIcctrol3rtes in solution also increases rather 
quickly with increase of temperature, while the conduc- 
tivity of metallic conductors, oa the other hand, diminishes, 
but more slowly, as the temperature rises. 

In considering the passage of the current through elec- 
trolytes, it is convenient to distinguish two cases. First, 
let there be a steady, or at least permanent current, and a 
continuous evolution of the products of electrolytic decom- 
position (these are called the " iont," anion and cation at the 
r anode and cathode respectively). The anunirU of ion thai 
appeari at an electrode in a second i* equal to the itrenglh of 
fht airrent (tuppoted conetant during a second) multiplied 
by a eomtanl called the electrochemical equivalent of the ion 

The electrochemical equivalent is proportional to the 
chemical equivalent, account being taken of the " valency " 
of the ion. (See art. ELE<7rK0LYSis.) 

For initance, if C bo the streDf^h of the cnrrent id the tllnstrn- 
tive cau above, then the amonnt of zinc deposited at the cathode 
in time ( wilt be iC^ and the amouDt of chlorine liberated at the 
•nods eCl, where t and c the electrochemical equivalenta of zinc and 

cbloiiiu^ and « : e :: w: 35'G, zinc being divalent. If a cell con- 
taimng Lead chloride (PbCI,) were alio inserted into the circnit, 
the nuM amount of chlorine would be liberated at the anode, and 
the amount of lead precipitated at the cathode would be pCt, where 

»7 65 
y : » : e :: -g- : 3 : 356, U. :: lOSS ; 82-5: 3SS 

f As the electrochemical decomposition ("electrolysis'^ 
i goes on, the surface of the electrodes is altered. In some 
cases the ion is merely deposited on the electrode, in other 
cases it combines more or less intimately therewith; but 
in general there is an alteration of the nature of the con- 
tact, and a consequent alteration of the electromotive force 
at the snrface of the electrod& Experiment shows that 
this electromotive force, in a great many cases, tends to 
oppose the passage of the current. So that if we insert an 
electrolyte into any circuit, the current starts with a certain 
Tilne, and falls more or less quickly, until it reaches a limit 
at which it remains steady. The opposing electromotive 
force of " polarization," as it is called, has then reached its 
maximum, and the deposition of the ions goes on without 
farther alteration of the contact surfaces. It is obvious that 
this limit may be reached under a variety of different cir- 
cumstances {vide infra, p. 86). There is also another pheno- 
menon, the possibility of which we must not overlook, 
nx., an alteration of resistance, owing to the presence of 
tho ions at the electrodes. This resistance, due to the ions, 
has been called the "transition resistance." The enfeebling 
of the current by the electromotive force of polarisation 
■night, as far as Uie obeerved result is concerned, be due 
. entirely to an increase of resistance, or to n transition resist- 
ance, and such wu the explanation given by the earUer 
piiTaidsta, It ia euy i howevu, to ihow that there is an 



actual electromotive force of polarization ; for, if we dia- 
engage our electrolytic cell from the battery, and connect 
its electrodes with a galvanometer, a current is indicated, 
which passes through the cell in the opposite direction to 
the original current. This could not be due to any tran- 
sition resistance, but must arise from an opposing electro 
motive force generated by the passage of the battery 
cnn^nt This point can be illustrated by a hydrodynami- 
cal analogy. If we attempt to force water through a 
narrow capillary tube, or through a wide vertical tnbe 
against gravity, there is an opposing force in both cases. 
But, when wo remove the pressure, the water has a ten- 
dency to rotum in the latter case, but none in the farmer. 
The former case represents a transition resistance, the 
latter an electromotive force of polarization.* 

Without denying the existenco of a transition resistance, 
we see that an electromotive force of polarization actually 
exists. In some cases, e.p., amalgamated zinc in zino 
sulphate, it is very smalt; in other cases, e.g., platinum 
electrodes in dilute sulphuric acid, it may considerably 
exceed the electromotive force of a Darnell's element. 

We have, up to this point, been treating the case where 
a permanent currant finally flows through the electrolyte ; 
but thera ara cases whera the existence of such a current 
would violate the principle of the conservation of energy. 

Suppose that a single Daniell's cell is the electromotor, then (sea 
below, p. BO) it a current C is sent for a time (, on amount of energy 
dCi is absorbed in the cell, d being conitant Suppose, farther, 
tbsl the excess of the inlrinaic eacrg; of the iocs, id the state in 
which thejF are being delivered in the electrolytic cell, over that 
which thiy po!ueu whea in combinstion is u>, then if a current C 
pass for a time I, an amonnt of energy wCt will be evolved. Bot if 
vC>d, this cannot go on for any time however ahoit, no matter 
how feeble the current may be, otherwise more energy would bs 
evolved in the cell than is absorbed in the battery. 

If we insert an electrolytic cell containing dilute snlphurio 
acid along with a galvanometer into a circuit in which 
there is a single cell of Daniell, we observe the galvano- 
meter needle swing out vigorously, and then settle down to 
a small and gradually decreasing deflection. The cnrrent 
ultimately becomes zero ;^ bnt the time it takes to do so 
may be considerable, and varies with the nature of the 
electrodes. If we remove the buttery after the current has 
stopped, and connect the polarized cell with the galvano- 
meter, we observe an initial swing very nearly equal to the 
former but in the opposite direction, and a corresponding 
deflection, which after a time disappears entirely. Althongli, 
as a rule, a sensible time elapses before the polarization 
reaches its maximum, yet it is important to remark that it 
may rise to a very considerable fraction of the maximum 
in a very short time indeed. Edluud^ found that in a cer- 
tain case the electromotive force of polarization reached 
0'57 of a Daniell in about ^ of a second. Bernstein hHs 
recently arrived at results of a similar kind. He found, for 
instance, that platinum plates, polarized to 1 -SS of a Daniell, 
fell, when the resistance of the circuit was 7-46 Siemnns 
units, to 1-S7 in OOIII sea* This rapidity of the rise 
and fall of the polarization b of vety great importance, and 
has, we think, been overlooked by some experimenters. 

In cases where the polarization does not reach its maxi- 
mum, no liberation of gas or other ion is observed, such 
as is seen with a permanent current, and it might of course 
be denied that chemical decomposition takes place at all. 
We shall, however, assume that Faraday's law holds for 
this case also, and assert that the cnrrent in the first 
instance actually passes through the liquid and produces 
chemical decomposition, according to the same law as » 
permsnent current, and that this goes on until the accumu- 

1 UaiweU, EUetrieitg, vol. L S 208. 

■ Far an exception to tikia itatamant m> Mow, p. 87. 

* foffg- ^"^ IxxzT., 1862. * Pagg. A»n^ civ., ISiE. 



48 



ELECTEICITY 



[kuctrio ocBxir^ 



lation of the iona fau generat«d an opposing electromotive 
force, equal to that of the battery, when of couise the cnr- 
reaC must stop We cannot justify this position very easily 
by direct experiment; yet there are many facts to support 
it^ and so long as it is tenable it seems to afford the most 
philosophical view of the matter. 

Having explained the phenomena of polarization no far 
as is necessary for our immediate purpose, we now proceed 
to inquire how far experience juatifiee the application of 
Ohm's law to electrolytes, or, which is much the same thing, 
to examine how fat the methods of different physicists for 
measuring electrolytic resistance have led to concordant 

Hea- One of the earliest methods, in which polarization was 

*""■ eliminated, was that of Horsford,' He filled a rectangular 
3tcU»^ trough with the electrolyte, and inserted in the trough two 
iftic electrodes very nearly fitting the cross section. These 
mitl- electrodes could be set at different measured distances 
""^ apart. They were coated on the further side with non- 
J^^ conducting substance, so tliat the current could flow between 
the opposed sides only. In this way he secured that the 
stream lines in the neighbourhood of the electrodes should 
depend as little as possible on the distance between them. 
This trough was inserted in the battery circuit along with 
a tangent galvanometer ; then the diBtance between the 
plates was decreased, and a metallic resistauce R inaerted 
in the circuit, so as to bring the current to the same 
strength as before. The current being the same in both 
cases, it is assumed that the polarization in both is the same, 
in which case the resistance of a length of the electrolyte 
equal to the difference of the distances between the elec- 
trodes in the two cases is equal to R. Knowing the section 
of the trough, we might calcolate from R the specific resis- 
tance of the electrolyte. If the values arrived at be the 
same when deduced from different lengths of the electrolyte, 
and for different strengths of current, it may be concluded 
that Ohm's law applies. The application of this method 
requires the passage of a permanent current, in consequence 
of which the ions appear at the electrodes, and the solution 
in the neighbourhood becomes altered; so that it is difficult 
to make certain that the polarization is exactly the same in 
the two cases, and that no resistance of transition is gene- 
rated. Matters may be mended a little by passing the 
current for the same time in both cases ; but this is scarcely 
a satisfactory remedy. Still valuable results were obtained 
with this method by Horsford and Wiedemann; the latter, 
ID applying it to silver and copper solutions used electrodes 
of aQver and copper respectively, whereby the polarization 
to be eliminated was very much reduced. 

Taking advantage of the discovery of Matteucci and Du 

Bois Reymond,* that carefully amal^mated zinc electrodes 

in a neutral^ solution of zinc sulphate are not polarizable, 

Bnti. Beetz* determined, by means of Wheatstone's bridge, the 

resistaDce of various solutions of this electrolyte. 

The liquid was inclosed in ■ cjliiidricil tube, 297 cm. long, with 

ji section of I'40&1 sq. cm, Amalgiiuated ' ' 

' " ■' ' " ■' obe, and fastened oi 

in«rted tigbtly inh , . , 

sides of two bottles wliich were filled with the Bolntion (tin 

that contained tn the tube). The thick electrodes leading to the 
discs, and the backs of the zinc discs themselves, were lacquered, to 
insolats them from the liquid in the bottles. Tht whole appantui 
waa immersed in a tiotigh of water, which conld be heated to any 
desired temperstore. 

In the courae of bta exp«Tuneatt Beeti demoostiated the absence 
of polarization when anulgamated zinc electrodsi are used, and 
elimiunted the transition resiitance b; boiling the electrodei in linc 
•olphate, and transferring them to the end* of the tube without 
exposure to the air. 

Beeti farther proposed to find the specific condnctivitj of other 
electrolytes in terms of that sf liQC suphate, by experimenting on 



closed circoits conmsting tnHnly of the electrolyte U 
He tried damping eipenmenta for this purpose, bat t 



Paalzow' inclosed the electrolyte to be e 
siphon, the two ends of which dipped into vessels of poroos 
clay also filled with the electrolyte. The clay vessels were 
immersed in beakers filled with zinc sulphate, at the 
bottoms of which were placed large amalgamated zinc discs, 
which formed the electrodes. The only polarizatioo or 
transition resistance to be feared is that at the bonndaij 
of the two liquids, and this is very email What little 
remained was eliminated, as in Horsford's method, by 
taking differences. 

The resistance of the whole arrangement was measured by means 
of Wheatstone's bridge, and then the Biphon wis replaoM by a 
shorter one filled with the same liquid. If R,, B.be the reaiataDcca 
found in the two cases, R, - R, is obviously the resistance of a 
length of the electrolyte equal to the dificreace between the length* 
of the siphoQS. If R,', B, be similar Talues obtained when the dee- 
trolyte is replaced by mercury, then the specific resistance of the 
electrolyte is i^', "„', -■ tlist ot mercury being taken as unity. 

The most important of all the recent researches on the KoU 
application of Ohm's law to electrolytes are thoae of F. ""^ 
Kohlrausch and NippoldL In order to avoid the effects ^! 
of polarization, they used the alternating cnrrenta of on S^ 
electromagnetic machine. These currents varied very didt 
nearly as the sine of the angle of rotation, and conld be 
sent in rapid succession through the electrolyte. The 
whole quantity of electricity that passes in the first part of 
any alternation is exactly equal and opposite to that 
which passes in the second ; hence equal quantities of the 
two ions (say H and 0) will be separated at each elec- 
trode. If the Hj and combine to form water, it is 
obvious that, on the whole, there will be no resultant elec- 
tromotive force of polarization either way ; and if they 
coexist side by side without combining, there will still be 
no rMolUmt electromotive force, provided the electrodes be 
exactly similar. There are two advantages in this method. 
There is no evolution of gas or other ion, and consequently 
no alteration of the solution and electrode, such as goes on 
with a constant current. We have, besides, another great 
advantage, which is denied ^ us with constant currents, — 
viz., that by increasing the tiTe of the electrode, we can 
diminish the effects of polarization. 

The whole amount of electricity which passes in each induction 
current is the same, and consequently the whole amount of ion 
deposited on the electrode is the sotne; hence, if we increase the 
surface ot the electrode, Ihe densitv of the deposit is decreased in 
an inverse ratio. Now, the researches of Kohlrausch and Hippoldt 
have shown' that, within certain limits, the electromotive force is 
proportional t« the surface density of the deposit Hence, by 
sufficiently increasins the surface of the electrodes, the polaniatioD 
may be made as small w we please. 

In the earlier Biperimenls platinum electrodes, having a surface 
of 1'08 cm. were Used, and it was found that each induction cnr- 
rent of the magneto-electric machine deposited on each squire 
millim etre ol the positive electrode onlyjj—^ c.cm. of oxygen. 
It was therefore expected that the iwlarization would be insensible, 
and that the elec^lyte would behave like a metallic resistance. 
The magneto-electric machine and the electrolyte were cotmeoted 
up with an electrodynamometer, and it was found that the deflec- 
tion of the suspended coil of the electrodynamometer was scarcel; 
sensible when the machine made 10 revolutiooi per seconilC 
tIthoDgb it was 16 scale divisions when the electrolyte was replaced 
._ -„ „ „. ., ^^ 



On the other hand, when the v 



bj 70 Siemens i: 



however, that when the surface of the electrodes was ii 
29 cm. a metallic reaistance could be found, which nve the aiMM 
deflection (within errors of observation) as the electrolyte tor 
speeds varying from I'S to 76-9 revolntioiu per second. 



* PpSg. Aim., czzivl., 1S69. 

* The idvantigi gained even with constant cmrenti b; ii 
tlw liie of thi electrodai is, however, appreciabla (■•• below, p. B8). 

' PDm. Ann., ISrS, and " Jnbelbd.,^ 1874. 



OBM'e LAV.] 



ELECTRICITY 



49 



The above results seem to compel ns to one or other of 
two Goncluaiona,^ — either that Ohm's law doea not apply to 
npidlj- alternatiog currents, whore the maximum of polar- 
isktiou is Dot reacho'l, or else that the electromotive force 
of exccedinglf amall depoeits of the ions must be very 
considerable. The fact that, uader certain coaditioDs, the 
electrolyte ia apparently a better, and under others, appa- 
rently a worse conductor thau a certain metal wire, seems 
at first sight rather to point to the former conclusion. On 
the other hand, the result with the 39 cm. electrodes, is a 
direct verification of Ohm's law. Kohlraoacb, therefore, 
adoptod the latter concluaion, and justified his doing bo 
by special researches on the electromotive force of small 
gaa deposits. He showed that, with the currents he used, 
the electromotive force is proportional to the surface density 
of the depodt, and estimated that the prodncta of decom- 
position of ^ mg. of water per square metre would gene- 
rat* an electromotive force equal to that of a Daniell's 
calL It ia of the greatest importance to remark that tlie 
polarization effects, from which this result is deduced, must 
have arisen and disappeared in some cases in much less 
than ^ of a second. The anomalous behaviour of the 
electrolyte with small electrodes is explained by Koblrausch 
by taking into account the self-induction of the circuit. 

A little cotuidentioD will show tliat the elcctromotiTe force due 
to this cause ftlw>y* ojipoflea the electioinotive forM of poUrizatioii, 
wlieii the curreut strength is a simple harmonic fnnctioa of tbe 
tim*. Let i denote ths carrent atrenKth, reckoned positive in * 
given diraction, then, sccordieg to Konlrusch's law, the electio- 

notive force of polsriiatiou at time (is -p/ idt, where p is the 

electromotive force genentsd by the pssaage of* unit of electricity; 
' ts nine depends on the electrolyte and on the electrode being, 



let !t = -= ; then we may represent the electromotive force of the 
machine at time ( by —mo' I, and the electromotive force 
of self-iudnction by -9^1 where k end q are constants, the 

latter being the coefficient of self-induction of the circuit (m 
Slectromagnetiam, p.7S). If id be the whole resistance of the 
tdrcoit, we may write 



'V-'t-'/"- 



^i'i-n)" 

when tbe origin of time has been thrown bsck by 

^M deflection a of the dynsinometer is propottionsl to - / iM 
and may be written * 

Ah* 



""-*(£ -H'- 



Kohlrausch found that this formula completely accounted 
for all the peculiarities in the behaviour of the electrolyte 
(for the numerical verifications see the papers quoted). 
We see that the deflection is increased or diminished by 
the insertion of the electrolyte, according as n is greater 

or lees thau -. /-^, and, if «= -, /^, the insertion of 
the electrolyte makes so difference. Again, if n = oZ . / 3 



the deflection will be the same as if there were no extn 
current and no polarization. So that, for any given 
electromagnetic machine, working at any given speed, a 
certain electrolytic arrangement con be found, which will 
exactly eliminate the effect of self-induction, and thereby 
render the efficiency of the machine a muTimnTn, it u 
obvious too that, with a given electrolytic cell, the deflec- 
tion reaches a maximum when 
P 

this maximum was actually obeerved by Kohlrausch (l-c). 

Having due regard to these circumstances, Kohlrausch Tert •( 
and Kippoldt found that Ohm's law wss applicable to elm's 
their alternating currents, for electromotive forces varying'"- 
from over ^ to under -^ of a Orove's cell. By using the 
constant current of an iron-copper thermo-electric pair, 
they found Ohm's Isw applicable to tiuc sulphate with 
amalgamated zinc electrodes, when the electromotive force 
woe reduced to j aa ' jp y of a Grove's celL 

It is important to remark that the fact that the electro- 
lyte behaves like ft metallic conductor through a consider- 
able range of velocities of the sine inductor, is not a 
conclusive proof that the hist trace of polarization has 
been eliminated. 

In fact, let x be the ledstSDce of the electrolyts, W that of tlie 
real of the circuit, and w the metallic reaiitance that gives the same 
electrodynamometer deflection for n revolution* of the indnctor per 
second, then the above fonnola gives 



2W 



•tx + Jj^-ti^') - W+^M-SirW/' 



sines we nippose x very nearly - w. If now p be redocsd t< 
small i^ue, it may happen, especially for tolerably lugh speeds, 

that b£ci '" ^"7 small compared with pq, in which case x-v> will 
be independent of « thronffh a considerable tsuge of speed, and the 
electrolyte will be replaceable by a wire whose resistance is leaa than 
~ re^iesistonce <k the electrolyte by a small constant quantity. 



The earlier results of Kohlrausch and Nippoldt for 
sulphuric acid, iu which they used 29 cm. electrodes, were 
affected with an error due to this cause, amounting to 
about i per ceut In the later eipedments of Kohlrausch 
and Orotrian,' this error was finally eliminated by " pb- 
tinizing" the platinum electrodes. Kohlrausch hod found 
that, with " platiuised'' electrodes of only 1 sq. cm. sur- 
face, the polarization of the currents of his sine-inductor 
was insensible ; he therefore concluded that, with 25 sq. 
cm. platinized electrodes, the residual polarization would 
be fiuaJly eliminated To make quite certain, be instituted 
three tests, which were carried out on the method used in 
all the later experiments on this subject^ 

The Wheatstone's bridge arrangement was adopted. Fig. SS 
gives ■ scheme of the 
arrangement. The fluid 
and a rbeoatat ocriipy 
two anna of the bridge, 
the remaiiiing two con- 
tain each 100 Siemens 
units; A is the filed 
and B the suspended 
coil of the electiortyna- 
mametcr, and S ths 
sine-inductor. 

In this way, (1) 
the reaistanco of a 
receiver with 25 cm. ^t- **■ 

platinized electrodes was found, when filled first with 
H,SO. of maximum conducKvity, and secondly, with NaCI, 
the driving weight of the inductor being varied, ao as to 
give speeds of 10 to 1 00 revolutions. The results, reduced 




' Pogg.J*n.,t&'r., IS7G. 

■ Koblransch and Orotriao, Pvff- ''*«■, ettv, 187( ; Kohlrausch, 
aid., cUi., 1S7A. 

VOL — 7 



50 



ELEOTKICITY 



[bLBCTBIO CUBXESt* 



to a common temperature, were, for the HgSO^, 141*73, 

Ul-64, 141-52, 141-53, 14155, and, for the NaCl, ,i 

366-27, 366-23, 366*25, 366-21 Siemens units, with the 
driving weights 5, 7*5, 10, 15, 20 kgr. respectively. (2) The 
resistance of a solution of zinc sulphate was found, first, in 
Beetz's manner with constant current and amalgamated 
zinc electrodes; secondly, using alternating currents and 
the same electrodes as before; thirdly, with alternating 
currents and the platim'zed electrodes; the three results 
reduced to a common temperature gave 537-49, 537*41, 
537*20. The greatest divergence from the mean might 
have been caused by an error of ^ degree in the 
temperature measurement. The agreement may therefore 
be pronounced complete. We think that it must be con- 
ceded that the experimental methods just described have 
solved in a satisfactory manner the problems involved in 
the determination of electrolytic resistance. We have 
dwelt on them so long partly because nearly all the in- 
formation on the subject we possess has been obtained by 
their means, and partly because they present points of 
great theoretical interest. 

Another method has been employed by Ewing and Macgregor.' 
The electrolyte was inclosed in a narrow tube with wide ends, in 
which were set platinum electrodes. This arrangement was inserted 
in a Wheatstone's bridge, and its resistance measured in the usual 
way. The precautions against polarization consisted in o^rating 
with currents of verv short duration, sent through the bndge by 
means of a ''rocker'' worked by hand ; the resistances in the arms 
of the bridge were also made large, in order to reduce the rate of 
polarization as much as possible ; another essential feature of the 
method is the use of a '* dead beat" galvanometer with a mirror of 
very small moment of inertia. The paper of Ewing and Macgregor 
has formed the subject of a somewhat bitter criticism by Beetz,^to 
which Macgregor has replied.^ 

Battery Battery Resistance, — ^If the electromotive force and iu- 
resist- terual resistance of a battery in action were the same, 
""*• whatever the external resistance, there would be no diffi- 
culty in finding the internal resistance by Ohm's method. 
We have simply to give two diflferent values to the external 
resistance, and measure the current in the two case& The 
electromotive force does not appear in the ratio of the two 
current measures; hence, knowing this ratio, we can find the 
internal resistance. Or we may use an electrometer, and 
measure the difference of potentials between the two poles 
of the battery, first, when the external resistance is infinite, 
secondly, when the external resistance is R. Then, if r be 
the internal resistance, the ratio of the first electrometer 

R+r 
reading to the second is — p— , by Ohm's law ; hence r 

can be found. 
Dlfficol- Unfortunately, however, the electromotive force of a 
*^ i^ battery is not independent of the external resistance. In 
2^^" general, when a battery is circuited through a small resis- 
tance, its electromotive force is much smaller than when 
the external resistance is very great. This arises from 
the polarization set up by the passage through the battery 
of its own current, and possibly in some degree from other 
causes as well. There is also reason to beb'eve that the 
internal resistance of the battery is a function of the cur- 
rent This being so, it is clear that a theoretically satisfac- 
tory determination of battery resistance cannot be arrived 
at by such methods as we have described. Since, however, 
the increase of the electromotive force is very slow after 
the externa] resistance has reached a certain value, and 
since the alteration of the internal resistance takes some 
time, we can get in many cases measurements sufficiently 
accarate for practical purposes. A variety of methods 
have been devised with this object, and applied mostly to 
the so-called constant batteries. It must be remembered, 
however, that there is something indefinite in the term in- 

^ No observation made for NaCl in the first case. 

• TrvM. M.S^,, 1878. » Pogg. Atm., cUt. * Proe. HJSJS., 1875. 



temal resistance, unless the circumstances be given under 
which it is found. In the method of Von Waltenhofen, 
the battery is " compensated " by another battery so ar- 
ranged that no current passes through it ; and then this 
arrangement is slightly altered, so that a very small current 
passes through the battery. This amounts to finding the 
internal resistance for very small currents. The method 
of Beetz also involves the principle of compensation; 
two batteries are used, but the one whose resistance is to 
be found is compensator and not compensated. The circuit 
of the compensator is joined for an instant, and then the 
compensated battery is thrown in. The assumption in the 
method is that the electromotive force is the same in 
the first instant whether the battery is closed through a 
resistance K or a resistance B'. The results seem to justify 
the assumption, and to establish the practical value of the 
method ; but there are clearly limits to its application which 
it would not be very easy to define. Beetz himself shows 
that the electromotive force of a battery is greater when it 
is compensated than when it is compensating. A similar 
objection may be urged against the method of SiemenSy 
which again gives good results when properly used. We 
refer the reader interested in this matter to the sources of 
information already quoted (see Historical Sketch), and 
content ourselves with an accountof Mlmce's method, which, ICanot 
although subject to the same objection as all the others, ia ™«thoi 
very convenient for rough purposes, and is much employed 
in this country. 

Let A, 6, C, D be four resistances arranged in circoit, B being the 
battery whose resistance is required. Insert a galvanometer between 

AB and CD, and a circuit which can be closed and opened by means 

of a key between AD and BC. We that have an ordinary Wheai- 
stone*s bridge, with a key in place of a battery, and a battery in 
place of the ordinary resistance to be measured. Owinff to the pre- 
sence of the battery, there will be a current through uie galvmno- 
meter, which will deflect the needle ; this deflection is compensated 
by means of a magnet, and the needle brought back to zero. Then 
tne resistances A, C, D are arranged so thai the galvanomster is not 
affected when the key circuit is opened or closed; when this is so the 
key and galvanometer circuits are conjugate, and we have AC- BD 
= 0, from which we can find B, since A, C, D are known. In practice, 
however, it is impossible in the great migority of cases to rolfil the 
direction printed in italics. Suppose for a moment we had arranged 
the resistances so that AC - BD is very nearly but not quite zero, and 
suppose we close the key circuit, which had been formerly open, 
then, since this is not conjugate to the battery circuit, the external 
resistance opposing the battery is reduced ; hence its electromotive 
force falls, tlie current through the galvanometer is altered, and the 
deflection of the needle alters. At the same time there is a current 
owing to the fact that AC - BD is not exactly zero. These two eflects 
may either conspii-e or oppose each other. No data, so far as we 
know, have been obtaincu which would enable us to tell how quickly 
this fall in the electromotive force of any given battery comes on. 
In practice we see a sudden jerk of the galvanometer, and then m, 
slow swing. The former is due to the deviation of the bridge from 
balance, and the latter to the alteration of the electromotive force. 
It is easy to decide which is which, for the direction of the former 
can be cnanged by making AC - BD positive or negative, while the 
direction of the latter is not aflected in this way. This disturbing 
effect is very great with one-fluid batteries ; it would, for instance, . 
be a hopeless undertaking to measure in this way the resistance of a 
cell of Smee while sending a large current. The efiect is not so 
great with a Daniell's cell, and can be reduced ad libitum^ by intro- 
ducing metallic resistance into the battery circuit The effect 
having been thus reduced within reasonable Hmits, we operate thus: 
— Arran^ the bridge until the deflection owing to deviation &om 
balancel.is opposite to that due to the change in the electromotive 
force; then, by gradual adjustment, work down the initial jerk to 
nothing, so that the needle appears to start off on its slow swing 
without any perceptible struggle. When this state of matters is 

AG 
reached, there is a balance, and B — — -. Then subtracting fromB 

the resistance put into the battery circuit, we get the resistance of 
the battery. Of course this does not solve the problem of finding the 
resistance of any battery sending any current ; but we believe that 
as much can be done in this way as in any other. Various modifi- 
cations of Mance's method have lately been proposed, but their 
pradieal advantages over the original method nave acucelj as yet 
been wtablished. 



BMT8TAHC1.] 



ELECTRICITY 



51 



On Resistance in Oeneral. 



We have drawn no distinction between statical and 
dynamical electricity in our application of Ohm's law, and 
no such essential distinction has ever been proved to exist 
In proportion as a body is a good conductor for galvanic 
electricity, it is a bad insulator for statical electricity. In 
Iv of i^neral, however, bodies which are good enough insulators 
dae- to retain a charge of statical electricity are so bad conduc- 
^* tors that it is with difficulty that we can compare their 
conductivities by means of the voltaic current On the 
other hand, it is difficult by means of statical electricity 
to compare satisfactorily the conductivities of very good 
conductors. Determinations of the last-mentioned kind 
Aovf, however, been made by Riess {vide infra, — Heating 
Effects), and the results agree with those obtained by 
other methods. The insulating power of a substance 
depends practically to a great extent on the nature of its 
surface. The dissipation of statical electricity by insu- 
lating supports is due, in most cases, almost entirely 
to the conducting power of a thin surface layer of mois- 
ture condensed from the atmosphere, or of some product 
of chemical decomposition caused by exposure to the 
air, or of dust or other foreign matter accidentally de- 
posited. As far as high specific resistance is concerned, 
parafiKn, shellac, ebonite, and glass at ordinary tempera- 
tures would all be about equally good insulators ; but in 
practice they stand in the order in which we have named 
them. Paraffin and shellac surpass the other two in their 
power of preserving for a long time a clean dry surface ; 
ebonite is very good for a time, but ultimately its surface 
becomes covered with a layer of sulphuric acid, arising from 
the decomposition of the material; glass, again, is very 
hygroscopic, although white flint glass, when kept dry by 
artificial means, is said to be one of the best insulators known. 
aU. Highest in the order of conductivity stand the metals 
and their alloys. In this class of bodies the passage of the 
electric current is unattended by chemical decomposition, 
and the conductivity decreases as the temperature increases. 
Along with the metals may be ranked a few other bodies, 
which have anomalous conductivity, but are not decomposed; 
SQch as graphite, red phosphorus, chloride and oxide of 
lead under the melting-point, various stdphides and selenides, 
tellurium, and selenium. In the great majority of the 
bodies included in this supplementary class the conduc- 
tivity increases with the temperature ; the last two present 
aeYeral anomalies, to which we shall refer farther on. 
eiro- A second class of bodies is formed by those which are 
^ decomposed by the electric current. The specific conduc- 
tivity of these is much lower than that of die metals, and 
it increases when the temperature is raised. To this class 
belong, when in solution or in the melted state, most simple 
binary compounds composed of equal equivalents of two 
dements, and compounds derived from these by ** double 
decomposition" (see, however, art Electroltsis) ; also 
some sulphides which have an anomalous conductivity, 
and glass and some bodies like it, which in the melted 
■tate, and in the soft state preceding fusion conduct as 
electrolytes. 

Non-conductors, on the other hand, are : — ^All gases and 
▼^KNUB, whether at ordinary pressures or in what is called 
a vacuum, diamond, sulphur, amorphous phosphorus, 
amorphous selenium, fluid chlorine, bromine, solid and 
melt^ iodine, bichloride and biniodide of tin, sulphuric 
anhydride, solid silicic acid, oxide of iron, oxide of tin; 
most compounds that are not binary, that is, do not consist 
of an equal number of equivalents of two components, e.^., 
many organic compounds— etheric oils, resins, wood 
fibre, caoutchouc ; also " binary compounds " in the solid 
state. To these may be added pure water, pure hydro- 



chloric acid, &c, which are very bad conductors, if not 
absolute non-conductors. 

Before leaving this part of our subject, it will be inte- 
resting to throw together a few of the general principles 
that have been arrived at, and to give a few numerical 
results, which will convey to the reader an idea of the posi- 
tion of the different classes of bodies in the scale of con- 
ducting power. For farther details we refer to Wiede- 
mann's Galvanismus, 

Metal8.---{1.) It was remarlted by Forbes that the order of con- Spedfio 
ductivity is the same for electricity as for heat. The measurements resist- 
of Wiedemann and Franz have established that the ratio of the ance and^ 
conductivities for heat and for electricity is very nearly constant, tempent- 
not only for pure metals, but also for alloys. (See Wiedemann's tare oo- 
Oalvanismua, bd. i. § 194.) efficient 

(2.) The conductivity of the pure metals decreases as the tern- of metals., 
perature rises from 0" to 100* C., the rate of decrease becoming 
smaller towards the upper limit Matthiessen expresses the con- 
ductivity; by the formula Ar-Aro(l-o^+/86*), where it^ denotes the 
conductivity at 0? C, $ the temperature, and a and $ constants. 
He found that o and fi had nearly the same value for all pure 
metals in the solid state, with the exception of thallium and 
iron, and gives as the mean values for pure metals a— 0*00376470, 
/3- 0*0000083402. The values for iron are a-0'0051182, 
3-0*000012916; for mercury, o- 0007448, /B- 0*0000008268. 
Although there can be no doubt about the general agreement in 
the formulae for the different pure metals, yet the actual formula 
arrived at is purely empirical and must be used only between 0* 
and 100"* C. if we carried its application beyond, it would give a 
minimum conductivity for pure metals about 800** C. The direct 
experiments of Miiller and Siemens give no indication of such a 
minimum. The latter represents the results of his experiments 
(extending in some cases as far as 1000** C.) by means of the for- 
mula r— aVt + /5T- 7, where r is the specific resistance, T the ab- 
solute temperature, a, $, y constants. Kelying on a formula of 
this kind for platinum, Siemens has ^constructed a pyrometer for 
determining tne temperature of furnaces by means of resistance 
measurements. 

(3. ) As we have seen, the specific resistance of pure metals goes 
on increasing continuously as the temperature rises. At the melt- 
ing-point there is a sudden rise in the resistance, and after that the 
resistance goes on increasing with a smaller temperature coefficient 
than before. This is in accordance with the fact, that both the 
specific conductivity and temperature coefficient of mercury are 
smaller than those of the other metals in the solid state. BismuUi 
and antimony are exceptions to this rule, in that there is a sudden 
decrease of resistance at the melting-point According to the re- 
sults of L. de la Rive, the resistance of metals in general is about 
doubled in passing the melting-point We should therefore expect 
the specific conductivity of frozen mercury to be about 8*81, that of 
silver being 100. 

Alloys,— (I.) Matthiessen found that the metals could be divided Alloys, 
into two classes, according to the conducting properties of their 
alloys: <* 

a. Lead, Tin, Cadmium, and Zinc. 
fi. Most of the other metals — Bismuth, Antimony, Plati* 
num. Palladium, Iron, Aluminium, Sodium, Go 'J, 
Copper, Silver. 

Let V, t^ be the volumes, «, / the specific grayities, k, V the con- 

ductivities of the two components of any alloy ; and let « — — 'ZJ'* 

and h = 1/ » he called the mean specific gravity, and mean 

conductivity of the alloy. Then alloys of any one metal of class a, 
with any other of the same class, have very nearly the mean specifio 
gravity and conductivity calculated by the above formula. 

Alloys of a metal a with a metal 3 nave specific gravity and c<m- 
ductivity always less than the mean. If a metal a is alloyed with 
a considerable percentage of /3, the conductivity is not much altered, 
but if a metal /8 be alloved with even a very small quantity of a, 
the conductivity is greatly reduced. 

Alloys of the metals 3 among themselves have in general a con- 
ductivity much inferior to that of either component The con- 
ductivity remains constant through a considerable range of per- 
centage, but rises very quickly as the percentage of either metal 
approaches 100. This property is very marked in an alloy of 
gold and silver. Matthiessen recommended an alloy of two parts 
by weight of gold to one of silver for the reproduction ol the 
standard of resistance. The resistance of such an alloy would be 
very slightly affected by small variai^ons in its composition. 

Mercury, and melted metals generally, are not subject to th« 
foregoing laws. A very small percent!^ of another even worse 
conauctmg metal raises the conductiyity of mercury, bat the 



52 



ELECTRICITY 



addition of krger qiuutlUea of the foreign m«Ul lowers the con- 
iavtintj. 

(2.) The foriDulie for the tempemtore variation for alloys of the 
■Detail a amoas themselves agree very closely with the mean for- 
mula calculated from the mlume percentages. 

If P denotes the fraction of itself by which the conductivity at 0° 
exceeds that at 100° for an arerage pure metal (F-0-29307), and F 
the same fraction, observed in the case of any alloy for which the 
observed and mean or calculated condactinties at 0' and 100° are 
J-,, (,,„ and k„ iTiu— then, according to MattLieaaen, the following 
lelation holds for alloys of metals a among themselves, and metals 
among theinselves: — 

P: P ;!i,„:i,», 
or, which is the tame thing, K,, kc^, denoting resistances, 

R,„-ll.-B„.-R,- 
For allays of ■ with fi, the observed value of P is in general greater 
than Uiat calculated by this formulee. 
ESect at OfA<r Fhyiieal Conditvma afficting the Etaijlance of Solid Bodiu. 
ihyiical —Besides temperature, a varietv of other circumstances affect the 
c«uiU- specihc resistance of metala As a general rule, metals are worse 
Udd. conductors in the hard than in the soft state. Tempering steel 
increases its resistance considerably, but subsequent heating and 
gradual cooling reduces the resistance again. The resistance of a 
wire stretched ny a weight is increased more than can ba accounted 
for by the mere decrease of the section.' Winding on a bobbin has 
the same effect. The finer a metal is drawn into wire, the creater 
is its specific resistance in the case of iron, the siualler in the case 
of copper. Magnetization haa also in certain cases been found to 
affect the resistance. These effects were studied by Sir William 
Thomson ; the results of his researchas are given in his Bakerisn 
Lecture, I%il. Tratu., 1858. The eiperiments are very instructive, 
and many of them well worth repeating now that we have more 
delicate apparatus. The most curious case of alteration of resist- 
ance is that of tellurium and selenium. We have already men- 
tioned that selenium in the amorphous state is a non-conductor. 
After continued heating it passes into the crystalline state and con- 
ducts. Sale foimd' that the conduclivity of this crystalline form of 
selenium is greatly affected by light, and that, too, differently by 



series of eitMriments on the snbiect. a 



\axct root of the illuminating 



power, and is distinct from any beating effect He fonnd the rtaU- 
tance of selenium in one case diminished by a fifth when it «m 
eiposed to the l^t of a certain paraffin limp ; the cbancB in 
teQurium nudet similar circumstances was lii'lr- ^e foona that 
the passage of a strong current through selenium sets up a kind of 
polarization, whicb opposes a corrent in the same direction ■■ that 
which arodnced it, and aids a current in the opposite direction. 
This led him to suspect that the action of light might of itself start 
a current in the selenium, and he found that under certain circum- 
stances this is the case. 

Fluids. — The veriScation by the eiperiments of Kohlrauach and 4 
Nippoldt of Ohm's law for electrolytes, throogh a wide range of "■ 
electromotive force, has greatly increased the mterat of all data ■> 
relating to the resistance of IMs "class of conductors. We have no •« 
difficulty in working with electrolytes whose composition and physi- 1" 

„i _._._ .-, — f„.i.. J..B..:.. . .1 .ugjt (jj impogiible in the case *' 

electrolyte has, far beyond the of 
solid metal, a value as datum for physical specula- "> 
tions concerning the ultimate properties of matter, which underlie 
Ohm's law. We refer the reader to Wiedemann's OalmRismtu for an 
account of the earlier results in this deoartment of Pouillet, Uankel, 
Bec^nerel, Horsford, Wiedemann, Becker, Lenz, and Saweljew. We 
recommend to his notice particularly the careful experiments of 
Beetz on zinc sulphate (his temperature determinations are the mget 
extensive of the kind), also the researches of Psalzow, who eiamlntd 
the conductivity of various mixtures of two soiutiona, the condac- 
tivities of which had been separately determined. He finds that if 
H and K' be the resistances of the components, the resistance of the 

mixture is not s-rcl so that the current is not divided betweoi 
the liquids as if they were metals in multiple arc ; nor is It the mean 
of R and R', but it lies nearer the smaller of ths two, A ^TJlfT 
result was arrived at by Ewing and Macgregor.' 

Kohlraosch and Orotrian' have made the moat recent as well as 
the most extensive invest igations ; and we shall best describe the 
present state of scientific knowledge on this subject by gtving an 
analysis of their results sud conclusions. Their experiments deal 
with the chlorides of the metals of the alkalies and alkaline eartha. 
Kohlraosch has also eisniined a number of the commoner acids. 
For convenience we have transcribed the diagram given by Kohl- 
raosch, which embodies certain of the results obtaineaby himself and 
Grotriao. Fig 1 of the diagram gives the conductivitie* ' (i,,) at 




IW^gBB^aBaaggBBM—llM l— I 

rr/^iagfljBBMHaHH&gnHnilgSmssI 



Diagram illustrating Electrical Conductisitj, 



18° C. ; the ordinates represent k^s » lO*. except for scctic and tsr- 
1aric acid, where they represent t,, x 10' and t,, x 10' respectively, 
the abscisss represent percentages by weight in the solution of 
IICI, H^0„ NHjCl, ic. In fig. 2 the values of the temperature 



' Forrecent experiments on this subject see iVoC. ft. 5., Dec. 1876, 
d Jmia 1S77. AuthoriUes for some of the Other facts stated will be 
nod in Wiedemann, L g 207. 
» Pne. R. 3., 1873, * Pne. R. 3., wli. xxiii iii». xxr. 



coefficient ^^ \ for 18" C. are given by the ordinates, the absciss* 
being percentages as before. For convenience of drawing the coefi- 
cient of acetic acid is decreased by 001. 

The curves which appear in the diagram include all the distinct 
varieties ; and it will be seen that in all casea the conductivity varia 



.,cliv,, 1876, and clix, 1673. 



USmAHOK.] 



ELECTEICITY 



53 



MHitiiiiiotul; with the coiic«iitnt[on, uisppnach toiero for infiDitelj' 
•mIc solutioiu twiUK indiCBteil in all caita. The chloride* may b« 
dirided into two cliwM. (1.) C&CL and MgCl, reach maiimum 

■^ ■ -valoi 



twiuK indici 

iiiTiuEu laui it/Q cUnM. \i-j v&V'i* 

eouductiTitiei 1988 x 10-*, 1310 x 10-» at 18' C. /or pencDUm 2t 

uid 19 '8 reapectivdf , in each cue short of latuTBtioii. LiCi pro- 

btbly don the tame, and NaCl appaan to reach a maximmn between 

3S-9 p.c and ila aatunUon percentage 28'G. (S.) KCl, NH,CI, 

SiCl^ and BaCl| incnaae in condDcting power up to the point of 

■■tnratioii. 

Taking the best conductiDg aolutions, the order of conductiiitiea 
■■ NH.Cl, KCl, NaCl, UCl CaCl,, SrCl,, BaCl^ MgCL, the 
alkaline chlondes heading the lilt. A 25 p.c. solation of NH^Cl is 
in fact half u good a conductor as the beat acid solution known. 

It was found that, if the cocduttirily tor email percent^ea be 
repreaentadby i-ii;i 'tp^, so that ■ may be called tlu ipceifie cim- 
duetiviiji m loatery lolutioTu, then ■ raries inversely as the specific 
gravity, that ia, directly as the " apeciSc Tolume,'' 

The temperatare coefficients for the chlorides are very nearly in. 
dependent of the temperature. There is a slight increase for higher 
teniperetarea, which is moat marked in the case of highly concen- 
tnted and viscous solutions of CaCl,, MgCl,. 

For weak solntiona the coeHicienta are all very nearly equal ; at 
IS' C. the extreme value for G p.c solutions lies betimn ^ (for 
LiCl) and A (for NH^CIj. There is a tendency, aa seen by the 
curves, to a vslae A, or 022 for very weak aolutions. It will be 
noticed (aee t^le below) that this coefficient is much larger tbau 
"0039, which is aboat the corresponding number fur a pure metal. 

When the percentage is increased (rom &re upwards, the tem^ 
Mnture coefficient for 13° C. decreases at first for all the chlorides ; 
It reaches a minimum for NaCI, CaCl- HgCL, which belong to 
class (1) ; but there is no minimum for KCl. NH^Cl, BaCI,, which 
belong to class (2), and have no maiimum conductivity. 

ITie acids investigated were nitric, hydrocliloric, sulphuric, phos- 
phoric, Dislic, tartaric, and acetic. In every case, eieept that of 
oxalic acid, a maximum conductivity waa obtained. The order in 
which we have named the acids is that of the condnctivity of the 
best conducting aolutions at 18° C. ; for the first three we have 
respectively i:.,10"-7330, 7174, 691*, the corresponding percen- 
tage* being 297, IS'S, 304, so that the maxima are vei7 nearly 
anal, and the maximum percentages not far apart. The curve for 
Ipburic Mid is exceedingly remarkable. Between and 100 p.c. 
of k,304, it show* two maxima. The first minimum occurs at 
the percentage corresponding to the hydrate II,BO^-^It,0. The 
conductivity correaponding to 11,30^ is also a minimum; for when 
80, u added, canung superaaturation, the conductirity again in- 
ei««w«, there moat therefore be ai Uaai one more maiimum, since 
DMlted 80. is a non-conductor. There is no peculiarity in the carve 
eonamonduig to the hydrate 2H,0 + H^0„ which is distinguished 
Cram HfO-f HjSOf in not being cryetallizable. A striking 
lari^ in the eaae of sulphuric and acetic acid i 
the curves of raitlance and of folidi^atlion Ui 
the latter is high, the formeris so alio; thereii 
«aaw for H.O-t-U^. and for H^0«, and i 
case* near n'G p.c ; the other minima do not agree 

A lemarkable relation ia given, which appears to tuuuevi. luc 
leutuoe of the monobasic acids HCl, HBr, HL, and HNO,. If 
ny pereentage b« mtiltiplied by the niecific ^vity of the solution, 
attadlTidedbythsmolecul^weightof the sciu, the result is thenum- 
ber of mtJecaJea (») in unitof volume of the solution. Onfonning 
• t^de <^ reaistances with n for argument, it was found that for 
Mthiticint with the same n, whether of HCI, IIBr, III, oi HNO„ 
the conductivity is the same. This appears very clearly from the 
dotted ourve in fig. 8 al the diagram, calculated from the different 
■dda, the rwulan^ of the carve, and in parts the coincidences, 
■n Terr muked. This result may be stated thus -.—In solulumt 
tmMtti»g om iqual ttumier of moUtuia, vheOxer of HNO), HCl, 
HBr, ar HI, the eomponatU of lUarolynt under equal eUemmaHvt 
fireufttm in oppoiiu dirtctiona teith tquai Tclativt vtlocitia. > 

nit temp«r«tare coeScienCs for the four monobasic acids are nearly 
iqaal, and nearly independent of the concentration. The same 
ineiSMe of temperatare coefficient with increase of concentntion 
M «M noticed in ^e case of viscous chloride solutions uipeais also 
ia tlw Tiscoss acid aolutions of phosphoric, tartaric, ana anljihnric 
Mid. It b also found that where the conductivity is a minimum, 
the tamperatnre coefficient ie correspondingly great; so that, with 
increasing tern peratnrelhemaxima and minima tend to get smoothed 
oat. It appsara also ttast the proximity of the maxima for H^O,, 
UNO), HCl, becomes more marked as the temperature rises. 

The existence of the maxima in most casea, and of the minima in 
the sulphuric acid curve, led Kohlrausch to suggest tlie principle 
that no stable diemical compound in a pure slate is a conductor, 
and that mixture of at least two sach compounds is necessary for 
eondaction. He mentions many instances of this principle, t.g., 
water, nil^nroas acid, carbonic acid, acetic acid, metlea boracic 



acid, chromic acid, anbydreos SO^ fcc. In a recent P<iper' he gives 



remarked between 
herever 
in both 
in both 
weU. 



oondootivity he got 
for water was 71 (H^-10'*). This waa after can^ parific*- 
tion and repeated distdlation in class, and finally in platinnm 
Teasels. After standing under a 'glass bell jar for 4'3, 20, 7B, 
and 1060 hours, the water rose in conductivity from 78 to 133, 8G0, 
850, and 3000 respectively. He calculatea that, if pure water were 
■ non-conductor, the presence of O'l mgr. per 11^ of HCt would be 
Bolficient to account for the observed conductirity. He also found 
conductivities for SnCl, (<) 200, alcohol (commercial distilled) 30, 
acetic acid {glacial melted) 4, ether (<) 8. Among recent researches 
of interest may be mentioned Brailn's attempt' to measure the coii- 
dnctivity of melted salts, and Grotrisn's'oa the relation between the 
viscosity and the electric conductivity of electrolytes. For the 
spcculationsof Kohlrausch, Hankel, Beetz, Wiedemann, and Quincke 
on the ultimate nature of electrolytic resistance, see the papers of 
the first-mentioned, or Wiedemann's Oaltanitmus, Bd. i. § 434 ^. 

Otua, — We are not aware tliat any experiments have hitherto Q^f^ 
established that any gas or vapour at ordinary temperature and 
pressure is a conductor. Boltxmann* has arrived at the negative 
result that air at ordinary temperature and pressure must have a 
specific resistance at Itaai 10** times that of copper. Sir William 
Thomson has, we believe, arrived at a similar result for steam ; and 
recent experiments by Prof. Maxwell' on air, ete«m, mercury, 
and sodium vapour (at high temperatures) have led him to a similar 
negative Conclusion. It was found, however, that the heated air 
from ■ Bunsen's burner conducts remarkably well.' The so-called 
unipolar conductivity of flames presents many anomalies, which 
have been examined by various experimenters. For the lilereture 
see F. Braun, Fogg. Ana., 1876. 

It would appear, therefore, that the loss of electricity from in- 
sulated conductor? at moderate potentials, observed by Coulomb 
andRiesa, cannot be due to coniiaction or convection by the air. 
but must arise almost whollv from the insulating supports. War- 
burs, who has experimented much on this subject, appears to be 
of the same opinion [vidt Boltzmaun, l.e. p. 415). Varley has lately 
investigated the passage of the current of a large number of Daniell's 
cells through s Geissler's (hydrogen T) tube. He fonnd that it 
required 323 cells to tiaii the current, but that once it was started 
it could be maintained by 308 cells; the current wbich Rowed was 
proporiionol to the excess of the number of cells over 304. Thus, 
for 317-301-4- 13 the current was proportional to 25}, for 330 
- 304 -^ 28 it was proportional to 61. Accordingly, if Ej be a con- 
stant, and R another constant (the resistance of the gas I) we get for 
the electromotive force E, required to send a current 1, E = E, 
+ RI. Eg is analogous to the electromotive force of polariiatiou. 
For further details about the resistance of dielectrics we refer the 
reader to Uaiwell's Elatncity and JUagrutism, vol. i. g 366 iqg. 

The following table will give an idea of the conductiiig power of (jeaenl 
different bodies ; r denotes the speciGc resistance in C.G.3. units (to table- 
reduce to ohms divide by 10*) ; a is the percentage of itself that r 
increases in tbe case of metsJs and decressca in the case of elec- 
Irolylea per deg. C. ; f ia the temperature at which r is given. 



i ' 


r 






20' 

20 
20 
20 
20 
20 
20 
20 

200 

400 

24 




1621 
1616 
16G2 
91GS 
9827 
19850 
21170 
M190 


■88 
■0* 
■07 










Lead (pressed) 


German silver. 


ZnsJ),(max.TOl'u!)!!!*!*!!.!! 


2GGX10' 1 1-5 1 
26 60 X 10* 1 Z» 
120-20x10* i'Z 
ISGxlO" 
227x10" 
73G X 10" 1 








Guttapercho 


3G3 X 10" 

7xl0»* 


1 



, __, seinthecaseof H, , 

by the solution becomes in reality a mixture of different componnds. 
—Pogg. Antt., civiii. 1876. • Pegj. Ann., cliv., 1876. 

* I'ogg. Ann., clvii., 1876 ; clx., 1877. 

* Fogg. Ann., civ,, 1875. ' Unpublished results. 

' Herwig {Fogg. Ann., 1874) has recently concluded from some ex- 
' 'g vapour doa conduct In a certain anomaloni way. 
were complicated by the conductivity of the gtaas 
tnbes containing tbe heated vapour ; steps were taken, however, to 
•liounats thla. Copsidenbla doubt hangs over the whole subtaot. 



E 



54 



ELECTRICITY 



[hxatino XmCEBb 



On ike Passage of Electricity through Insulators, 

Dlvnp- Hitherto we have divided bodies into conductors, through 
ttye dii- which electricity passes under the influence of any electro- 
^^^^^9^' motive force, however small, and non-co7iductors or insulators, 
through which electricity will not pass, no matter how great 
the urging force. In practice, however, when the value 
of the electromotive force reaches a certain limit, electricity 
does pass through a non-conductor. A discharge of elec- 
tricity taking place suddenly in this way through a non- 
conductor is called a " disruptive discharge,^* The power 
of a non-conductor to resist up to a certain limit the passage 
of electricity through it has been called its dielectinc 
strength. The dielectric strength of any medium is greater 
the greater the electromotive force it will stand, when 
placed say between two parallel metal plates arranged in a 
^yen way, before it is broken through by the disruptive 
discharge. We shall by and by attach a definite quanti- 
tative signification to the term, but the general notion will 
be sufficient for the present. 

Although it may be found when both phenomena have 
been more fully analysed, that conductive and disruptive 
discharge are really two different aspects of one and the 
same phenomenon, yet for the experimenter they are two 
distinct things, which must not be confounded. 

This would be the place to set forth the quantitative rela- 
tions which regulate the electromotive force required to pro- 
duce disruptive discharge, the quantity of electricity that 
passes under given circumstances, and the dielectric strength 
of different media; in fact, to lay down for disruptive dis- 
charge a law corresponding to the law of Ohm for metallic 
and electrolytic conduction. The present state of electrical 
science, however, does not permit us to do this in a satis- 
factory manner. Experiment has not as yet led to a single 
dominant principle, like Ohm's law, which will account for 
all the phenomena of disruptive discharge. The best theory 
of the subject is Faraday's, which will be gone into under 
"disruptive discharge in gases" Observation and experi- 
ment, on the other hand, have been occupied for the most 
part with the various transformations of energy which ac- 
company the disruptive discharge. We prefer, therefore, 
to discuss the whole matter under the single head " disrup- 
tive discharge." 

TRANSFORMATIONS OF ENERGY ACCOMPANYING 
THE ELECTRIC CURRENT. 

Under this head we propose to discuss (to use a word 
of Hankine's) the energetics of electricity. It may be 
objected that this heading might have been put over a 
good deal of what has gone before, and we shall, for con- 
venience, treat certain matters under it whieh, in a strictly 
logical division, would have found a place elsewhere. If 
we had formed a definite conception of what we call elec- 
tricity — had, for histance, assumed that it is a material fluid, 
having inertia like other fluids, then no doubt the energetics 
of the subject could have been much extended. As it is, 
we think that advantage is to be gained by associating in 
our minds the experimental laws which we are now to 
arrange under the above heading. 

We shall consider (1) the heat developed in metallic and 
electrolytic conduction, and at the junctions in heteroge- 
neous circuits ; (2) the mechanical, sound, heat, and parti- 
cularly light effects accompanying disruptive discharge; 
(3) the energy of magnetized iron and steel, and of electric 
currents in the neighbourhood of the electric current (electro- 
magnetism) ; (4) the energy of the electrotonic state, or 
electrokiuetic energy (magneto-electric induction). In this 
list ought to be included the potential energy of chemical 
separation, which would come under the head of electrolysis. 
At present, however, electrolysis is quite as much a chemi- 



cal as an electrical subject^ and it has been found convenient 
to treat it in a separate article (see Electrolysis). Some 
points in connection with it have already been touched 
upon, and a few more will come up in (5), which treats ol 
sources of electromotive force, and deals with the ques- 
tion, whence comes the energy which is evolved in the 
voltaic circuit 1 a question the answer to which is for the 
most part experimental and practical — ^the only one, in fact^ 
that the state of electrical science permits us to give. 

Heating Effects, 

It is easy to show, by a variety of simple experiments, Derd 
that a current of electricity heats a conductor through >d'|^. 
which it passes. In the case of moderately strong currents ^^ 
the heat developed is perceptible to the touch ; the wire 
may, in the case of very strong currents, be raised to a 
white heat ; it may melt, and even be volatilized. In the 
case of very weak currents, the heating effect may be de- 
monstrated by passing the current through the spiral of a 
delicate Breguet's thermometer. We find, when we 
examine the experimental data on the subject, that heating 
effects may be conveniently divided into two distinct classes. 
In the first of these the fundamental law is that the de- 
velopment of heat in any part of a linear circuit varies as 
the resistance of that pajii multiplied by the square of the 
current In the second class the development of heat 
varies as the first power of the current. The heating effects 
of the first class are obviously independent of the direction 
of the current, and are irreversible; and the more we 
examine them the more they appear to correspond to the 
loss of energy by the f rictional generation of heat in ordin- 
ary machines. In the language of the dynamical theory 
of heat, the part of the energy of the electric current 
which disappears in this way is said to be dissipated. 
The effects of the second class change their sign when the 
direction of the current is changed ; so that, if anywhere 
there was evolution of heat when the current flows in one 
direction, then, when the current is reversed, there will be 
absorption of heat to an equal extent We shall find that 
we have great reason to believe that such effects are 
strictly reversible.^ In order to get a satisfactory founda- 
tion for the simple theoretical views which we have thus 
indicated, it is essential to be able to separate the two 
classes of effects. Now, this is possible to a veiy great 
extent even in practice. The effects of the first class in- 
crease much more rapidly with the strength of the current 
than those of the second, so that, by sufficiently increasing 
the current, we can make the effects of the second class 
as small a fraction of the whole heating effect as we please; 
while, on the other hand, by sufficiently decreasing the 
current, the preponderance of the second class may be 
increased to any desired extent. We shall in what foUows 
suppose the two classes of effects separated in this way. 

Discharge of Statical Electricity, — One of the earliest Haitii 
attempts to study the heating effects of the electric dis-^^ 
charge was made by Kinnersley. He constructed ancimii 
thermoelectrometer, which consisted of a closed glass 
vessel, in which were fixed two metal balls communicatiog 
with electrodes outside the vessel The bottom of the 
vessel was filled with a little coloured fluid, which com- 
municated with a tube having a vertical arm rising outside 
the vessel. When a spark passed between the balls, the 
heat developed caused the air to expand and force the 
liquid into the vertical tube, the rise of level in which indi- 
cated the degree of expansion, and, by inference, the amount 
of heat developed in the spark. 

Sir Wm. Snow Harris* revived this instrument of Kin- 
nersle/s, and improved it by stretching a fine wire between 

1 Thut is, in the thermodynamic senae. * PhiL Tnms,^ 18S7. 



Hunira mnotB.] 



ELECTRICITY 



55 



TMf> the tennmals inside the Tusel, so that the heat meunred 
*!*■ "^ waf now that eTolved in a metallic conductor. 

With this improred imtmmeiit henudaannmberof Tsluible cx- 

CKDcntB OD tbe hMting of wiren b; the discharge of a, Leyden 
tterf, vboH chai^ wu mounred by a Iahe'* electrometer. As- 
Mtniiig tlut the heat developed rariei inversely u the conductivity 
of ths win (which is not the cose), be nrrHnged the metale iu ■ series 
which igT M g with that given later by Bleis, althoagh the nQmbera 
given do not properl]' represent the condnctivities owing to the 
erroDMlu usumpUon on which ther are deduced. Harris observed 
that the specific condactivity of uloys is often less than that of 
cither raetal, and that a very snull admixture of another metal con- 
aderably reduces the conductivity of pure eoppec. He alto arrived 
st the result that the amount of neat developed in a wire varies as 
the qnantity of electricity which passes in the discharge, but seems 
to have concluded that ue amount of hattery surface used had no 
effect^ 
^ Rien made two very important improvementfl oa the 

«ino- thermoelectrometer by subetitnting spirals for the straight 
^^ wire of Harris, and b}^ inclining the tube containing the 
' liquid so as to be nearly horizontal. The sensibility of the 
instrument was thus greatly increased. Biess took np the 
whole question of the heating oE wires, and investigated it 
thoroughly. 

The actnal iDstnuneot which he used is represented in figure 27 
(taken fhnn bis BeibungieltctrkUal). It consists of a gUss tube of 




Fig. S7. 



nanow bore, 10 to ]7 inches long, to which Is blown a glan globe 
S to 1 inches in diuneler. This tube is partially filled with some 
coloured fluid which conSnes the air in the globe , a wide reservoir 
at the other end of the tube allow* the Quid to accumulate without 
•eniible change of levcL The stand of the instrument consists of two 
pieces hinged together, so that tbe tube canHK placed at s small iu- 
elination to the horizon. Tbe rest of the instrumcDt will be onder- 
itood from the figure. Details concerning the msjiipujation will be 
found In the lUibangitUeirieilM, Bd. i. S ^10- when the fine 
wire is htated by a cnrrent of electricity, the heat developed is 
divided between the wire and the air ; the eipansion very quickly 
teaches a maiitnam, and the level of the liquid in the fine tube 
becomes stationary for a moment. If m be the nflmber of scale 
diviiioaa between its original and flual positions, we have (see 
BieM, Ic, or Mascart, t. i. g 325) 

T-mAU+0^Y andH-fia(CW+B) .... (1), 



beat developed by the current. C and W aj 



A very convenient form of thermoelectrometer, called the 
liermoiititre inaeripteur, has been used by Mascart (I.e.). 



' PkO. IVoM., 1834. 



Tbe alterations of preesnre are registered automatically on 
a revolnng dmm, after the manner of the pulse-regiatering 
instrument of Marey. One advantage of this instrument 
is that it gires a representation of the course of the tem- 
perature in the apparatus. 

In moat of his experiments Riess used batteries of Leyden 
jars. The jars were all as nearly as possible alike, and the 
inner armatures were in general connected together. The 
quantity of electricity given to the battery was measured 
by means of a Lane's jar, the balls of which were placed at 
a distance of about a line apart The battery was then dis- 
charged through the thermo-electrometer along with taj 
external circuit connected with it 

It is of great importance in such experiments as we are Qmm 
now describing to examine what happens at the place where «>>>^ 
the circuit is closed. This closure is effected by bringing*^"" 
two metallic balls into contact But before contact is 
reached, a spark passes in which sound, light, and heat an 
given forth, — in a word, energy evolved. When the resis- 
tance of the circuit is small, this spark passes at a consider- 
able distance, and is very intense, no matter how quickly 
the conductors are brought together. The energy consumed 
in this case is a considerable fraction of the ^vhole energy 
given out by the discharge. If, however, tbe resistance of 
the circuit through which the discharge takes place be con- 
siderable, the electricity takes longer to accumulate suffi- 
ciently to raise the electromotive force between the balls to 
the discharging limit We may, therefore, by operating 
quickly, get the balls very nearly in contact before thq 
spsrk passes. In this case the spark is much less intense, 
and the fraction of the whole energy which appears in it 
is very small Riess made some very valuable experiments 
on this point He arranged on air-break in the circuit of 
the thermoelectrometer, which he could widen or narrow at 
pleasure, and discharged his batteries through this circuit 
in the nsual way. He found that as the gap is widened the 
amount of heating in the thermometer is at first increased, 
but after a certain length of break is attained it decreases 
again. It must be remembered that we have now two air- 
breaks in our circuit of discharges, tbe discharging break 
and the inserted break. One effect of the inserted break 
is to diminish the intensity of the spark at the dischargiiig 
break, and cause a decrease of the energy which appears 
there. On the other hand it makes the discharge of the 
batt«iy incompUU, so that part of the potential energy is 
not exhausted. It is very likely to the opposition of these 
two effects that the peculiarity observed by Rieis is due, 
Mascart has observed a similar phenomenon in disruptive 
discharge through oil of turpentine. At oil events Bless 
showed that, when the inserted break was not longer than 
^ths of a line, the heating in the thermometer was the 
same as when there was no break at all Hence, if we 
make the resistance of our circuit so great that the spark at 
the discharger is not longer than ^ths of a line, tbe energy 
consumed there may be neglected. 

The resistance of the connections belonging to the 
battery and the thermometer were always very small com- 
pared with that of the thermometer wire, and the wire, if 
any, inserted outside the thermometer ; so that, if the resis- 
tances of these be R and 8, the resistance of the whole 
circuit may be taken to be R -i- S. The law to which the Chneii 
experiments of Riess led can be expressed by means of the I*v. 
formula 



=ir+s'J 



(3), 



where Q is the amount of electric potential energy which 
has disappeared, and H the amount of beat {measured hy 
its dynamical equivalent) developed in tho wire of the 
thermometer, whose resistance is S. 

In the case of the complete discharge of a batter; of n 



56 



ELECTRICITY 



[hiatino 



]an» each of capacity C, if g be the whole charge, we get 
immediately, from (48) of Mathematical Theory (p. 34), 



^"R+S* 20lt' 



. . (8). 



Hence, if we keep the thermometer and inserted wires the 
same, the thermometer indications will be proportional to 

?- , or, in words — the heat evolved in the whole or in any 
n 

given part of the circuit is proportional to the square of the 

battery charge directly^ and to the number of jars (i.e., to the 

battery surface) inversely. 

If the thermometer wire remain the same, while the 

length, section, and material of the inserted wire is varied, 

then, r being the specific resistance, I the length, and p 

4rZ 
the diameter of that wire, R= — j. Then, according to 

(3), the heat developed in the thermometer is given by 



H- 



rl 
1 + B4- 



. . (4), 



nrhere A and B are constants. 

If, again, we use two wires of the same material of 
lengths / and /' and diameters p and p', and make two ob- 
servations with these for inserted and thermometer wires 
respectively and vice versa, then, if Hj and Hg be the heat 
evolved in the two cases. 

Hi - V* <^^' 

since R + S is the same in the two cases. 

When the discharge is not complete, we have only to 
substitute for Q in (3) the appropriate expression for the 
exhaustion of the electric potential energy. Similarly we 
may find the heating effect caused by the discharge of a 
battery of jars arranged in series and charged by cascade 
inTranklin's manner (p. 35). If we discharge through 
a multiple arc, we may assume that the dbcharge divides 
itself between the branches in the ratio of the conduc- 
tivities, so that the conductivity of the whole arc is the 
sum of the conductivities of its parallel branches. On 
these principles it is easy to calculate the heat generated in 
the whole circuit or in any branch of the arc 

All the cases we have alluded to were treated experiment- 
ally by Riess, and satisfactory agreement with formula (2) 
established in every case. 
Compari- By means of formula (4) he compared the specific con- 
ton of ductivities of a variety of metals. A and B were determined, 
eonduc- gj^^ ^ standard wire of platinum of given length kept in 
^ ***■ the thermometer ; the wires to be compared with it were 
inserted in the outside circuit, and the heating in the 
thermometer observed. From the result the specific con- 
ductivity (in terms of platinum) of the wires could be cal- 
culated, their dimensions being known. The results agree 
very well with those got by other means. ^ 
Heating Heating by Constant Current — ^The heating effect of the 
*^^tlnt ^^^^^^ furnished by a voltaic battery was recognized as 
^g,^^^ a distinct and often very remarkable phenomenon for a 
considerable time before any definite quantitative law was 
established regarding it. Davy^ experimented on wires of 
the same dimensions but of different materials, and found 
that the metals could be arranged in the following order: — 
silver, copper, lead, gold, zinc, tin, platinum, palladium, 
iron, — those standing nearer the beginning of the list 
being less heated by a given current than those nearer the 
end. 



Joule' was the first, however, to establish a definite law ^drt 
connecting the amount of heat evolved per second with the JJJ^ 
current strength and the resistance of the wire. He wound 
the wire in which the heat generated was to be measored 
round a glass tube which was immersed in a calorimeter. 
The resistance of the water is so great that we may assume 
without sensible error that the whole of the current passes 
through the wire. The temperature of the water was de- 
termined by means of a mercury thermometer immersed in 
the calorimeter. The amount of heat developed in the 
wire per second could then be found by the usual calori- 
metric methods. The strength of the current was mea- 
sured by means of a galvanometer inserted in the battery 
circuit along with the wire. By experiments of this kind 
Joule established that the amount of heat generated im a 
given time varies directly as the product of the renstance of 
the noire into the square of the strength of the current. So 
that, if we choose our units properly, we may write 



H-RI*< 



(«)• 



> See Wiedemann's Oalvaniamm, Bd. L § 194. 
• ym. Trans., 1821 



where R is the resistance of the wire, I the strength of the 
current, and H the quantity of heat generated in time t. 

The experiments of Joule were repeated with increased precau- . 
tions against error by Becquerel,* Lenz,' and Botto. Becquerel 
allowed the wire to disengage heat till the calorimeter reached such 
a temperature that the loss of heat by radiation and convection, 
&c., was just equal to the sain from the wire, so that the tenipera- 
ture became stationary. The current was then stopped, and the 
loss of heat per second found by observing the fall of temperatore 
in the calorimeter. Botto used an ice calorimeter. Lenz* made a 
series of very careful experiments with a calorimeter, in which the 
liquid used was alcohol, which is a much worse conductor than water. 
He first cooled his apparatus a few de^ees below the temperature of 
the surrounding air, and then allowed the current to generate heat 
in the wire till the temperature of the whole calorimeter (which was 
kept uniiform by agitation) had risen to an equal number of degrees 
above the temperature of the air. The current was then stopped, and 
the time t which it had flowed noted. According to Joule's law, 
<RP ought to be constant, and it was found to be so very nearly. A 
very convenient instrument for demonstrating and measuring the 
heat generated by the electric current in a wire ia the galavano- 
thermometer of Poggendorff, which consists simply of an alcohol 
thermometer with alarge bulb, into which ia let a spiral of fine 
wire. The heat generated ia deduced from the expansion of the 
alcohol, which is measured by means of a scale fastened to the stem 
of the thermometer. The value of the graduations is found by com- 
parison with an ordinary thermometer. The thennoelectrometer 
of Riess might also be used in a similar way. 

Heating in Electrolytes. — Joule's law applies also to Elad 
electroljrtes. The phenomenon, howevey, is not so simple *J^ 
as it generally is in the case of metallic conductors. Dis- 
turbances arise, owing to the heat evolved and absorbed 
in the secondary actions that take place at the electrode ; 
and superadded to this we have in all probability an ab- 
sorption or evolution of heat corresponding to the Peltier 
effect between different metals, of which we shall have to 
speak directly. Joule eliminated these disturbing infla- 
ences by using a solution of copper sulphate with copper 
electrodes. In this case copper is dissolved from one elec- 
trode and deposited on the other, so that if we except the 
slight difference in the states of aggregation of the dis- 
solved and deposited copper, the secondary processes are 
exactly equivalent, and must compensate each other. Joule^ 
found that in a certain solution of CuSO^ 5*50 units of 
heat were generated in a certain time, while in a wire of 
equal resistance 5 '88 units were generated by an equal cur- 
rent in the same time. In a similar manner K Becquerel' 
found that a current, which would produce a cubic centi- 
meter per minute of explosive gas, generated in certain 
solutions of CuSO^ and ZnSO^ 0213 and 0365 units of 

* Phil. Mag., 1841. « Ann. de Chim, et de Phys., 1848. 

* Pogg. Ann., Ixi., 1844. 

* Wiedemann's Oalvantsmut, Bd. i. S ^70. 

' PhiL Mag., 1841. • Aim. ds Chim. ei de Ph^s., 1843. 



HKiTXNo xrracTB.] 



ELECTRICITY 



57 



heat ; while the same current would have generated in wires 
of equal resistance 0*26 and 0*32 units respectively. 
Itlcr RevenihU Heating EfftcU. — ^Peltier ^ was the first to 
Ml discoyer an effect of this nature. He found that, when an 
electric current passes orer a junction of antimony with 
bismuth, the order of the metals being that in which we 
hare named them, there is an evolution of heat at the junc- 
tion ; and, when the current passes in the opposite direc- 
tion, there is an absorption of heat, S3 that the temperature 
of the junction falb. Here, therefore, there is an effect 
which cannot vary as the square of the current strength, 
but must be some function of the current strength, whose 
principal term at least is some odd power. 

The Peltier effect, as it it now called after its discoverer, may be 
demonstrated by inserting a soldered junction of antimony and 
bismnth into a Riess's tnermoelectrometer. When the current 



goes BiSb, the fluid will rise in the stem, indicating absorption of 

heat ; when it goes SbBi, the fluid will fall, indicating evolution 
of heat Or we may use Peltier's cross, 
which consists ot two pieces, one of 

bismuth hW, and the other of anti- X — ^^^ 

mony AA', soldered together in the 
form of a cross (fig. 28). A and B are 
connected by a wire through a gal- 
vanometer O. A' and B' are con- 
nected with a battery C through a 
commutator D, by means of which the .^ 

current can be sent either from A' to /^""^i^^^^^^f 
W or from B* to A' through the junc- U i !) * 
tion. The thermoelectric current in- I'i*"**^ 
dicated by the galvanometer shows that ^ 
the junction is heated in the first in- 
stance and cooled in the second. *^*8- "8. 
By leading the current of a Grove*s cell for five minutes through 




a BiSb junction, Lenz' succeeded in freezing a small quantity of 
water which had been placed in a hole in the junction, and previ- 
ously reduced to 0' C. The temperature of the ice formed fell to 
- 4-6* C. 

irt of The Peltier effect is different for different pairs of metals. 
tier Peltier and BecquereP found that the metals could be ar- 
*^ ranged in the following order : — 



Bi, Gr,« Pt, Pb, Sn, Cu, Au, Zn, Fe, Sb . 

If the current pass across a junction of any two of these 
metak, cold or heat is generated according as the current 
passes the metak in the direction of the arrow or in the 
opposite direction ; and the Peltier effect between the metals 
is greater the farther apart they are in the series. We shall 
see later on that this is none other than the thermoelectric 
series. 

Von Quintus Icilius* showed that the Peltier eject is 
directly proportional to the strength of the current. He 
passed a voltaic current through a tangent galvanometer 
(serving to measure it) and a thermopile of 32 BiSb couples. 
The current was allowed to pass for a fixed time, then the 
battery was removed and the thermoelectric current of the 
pile measured by means of a delicate mirror galvanometer. 
The current of the battery heats the pile in part uniformly 
according to Joule's law : this causes no unequal heating 
of the junction, and therefore no thermoelectric current ; 
and in part unequally, so that one set of junctions are cooler 
and the other warmer than the mass of the metal : this 
causes a thermoelectric current, which, since the tempera- 
ture differences are small (see below, p. 97), may be taken 
to be proportional to the temperature difference, that is, to 
the double of the Peltier effect at each set of junctions. 

It is interesting to note the analogy here with the polar- 
ization of an electrolytic cell. We turn a battery on to 

^ Ann, de Chim. et de Phyt., 1834. 

' See Wiedemann's Oalvanismus, Bd. i. § 689. 

» Ann, de Chim, U de Phye,, 1847. 

• Qs-Oerman SUver. » Pogg. Ann., Ixxxix. 1868. 



the thermopile, and polarize it, as it were. Then, when we 
remove the batteiy and close the pile, we get a return cur- 
rent, which might be called the polarization current of the 
thermopile. 

In jB;eneral the Peltier effect is, as we have seen, mixed up with 
Joule^ effect, and makes itself felt by producing a diaturbuice at 
the junction. Thus Children* found that, when a strong current 
passed through two mercurv cups joined by a thin platinum wire, 
so that the wire became red hot. the temperature of the mercury in 
the cups next the + pole of the batte^ rose to 121* F., while in 
the cup next tiie - pole the temperature was only 112* F. Frank- 
enheim^ studied the two effects together. He made a Peltier's 
cross of the pair of metals to be examined, passed a current I through 
the cross first in one direction and then in the other, and deter- 
mined by means of a delicate galvanometer the thermoelectric cur- 
rent generated in each case, which is very nearly proitortional to 
the heat produced. If a and h be the heat from Joule and Pel- 
tier effects respectively, and t and H the observed thermoelectric 
currents, then t-C(a + 6), i'-C(a-6); whence a - (t + *")-:- 2C, and 
(«(t-i')-^2C. In this way he found that a was proix>rtional to 
P, and & to I. Thus the whole heat developed may be expressed 
bv aPdr&I. We get in this way a verification of the results both 
of Joule and of Yon Quintus Iciuus. 

Further experiments have been made on this subject by Thomson 
Edlund and Le Roux ; and Sir W. Thomson was led by a effect, 
remarkable train of reasoning to discover another rever- 
sible heating effect We prefer to leave these matters for 
the present, to return to them when we consider thermo- 
electric sources of electromotive force. 

The Peltier effect between metals and liquids and other 
reversible effects will also come un again under the Origin 
of Electromotive Force. 

Theoretical Deduction of the Formulas, — The above for- Theory 
mulaB for the heat developed in wires by statical and dyna- ?^ heat- 
mical electricity may be deduced from a common formula, ^^^ 
which can be deduced from Ohm^s law. 

Let P, Q be two points of a linear circuit, and let E be the differ- 
ence between the potentials at P and Q, then, if there be no other 
electromotive force in the portion PQ, the work done bv a unit of 
+ electricity in passing from P to Q is E. Hence, if I be the 
strength of the current, so that I^^ units of electricity pass from 
P to Q in time eU, then the amount dto of work done by the 
current in time dt is EIcU. But, by Ohm's kw, £=RI, hence 

dw^ViVdi (7). 

Since the whole of this work is spent in heat, we may for to write 
H, which denotes the heat^ ^nerated in PQ. If the current be 
constant, we get immediately JH = RI% which is Joule's law (6). 
If the current be variable, H=/RI*«tt, from which we may very 
easily deduce the formula for the discharfje of a battery of Leyden 
jars. For, applying Ohm's law to the whole circuit whose resist- 
ance is R + 8, we nave, if U denote the potential of the inside 

coatings at time /, I » . Also the capacity of each of the n 

jars being C, we have for the charge /-nCU, and l"-^ 
= nC^ . Henco 



V R+sy <tt R+S 2 



R ^ 
R+3* 2nC 



(8), 



where q and V have the same meanings as in (8). (8) agrees with 
(8), ezce|)t that we have reckoned the heat developed in a portion 
of the circuit whose resistance is R instead of S, as in (3). It 
appears, therefore, that the theoretical formula (7), when properly 
interpreted, covers both cases. 

If there were a junction of heterogeneous metals in the part PQ 
of the circuit, at which the potential suddenly fell by an amount 
n, then work equal to lildi would be done by the current in past- 
ing over the junction, and we should have to write 

dW-RP(« + nI(« W. 

Had there been a rUe of potential at the junction, we should have 
written - n instead of + n. If all the work done at the junction is 
transfa;med into heat, W — H as before, and for a constant current, 

H-RP< + nI< . ... (10). 



• PhU, Trans., 1815. ' Pogg. Ann., xvi. 1854. 

* Measured, of course, in dynamical equivalents. 

VHL — 8 



58 



ELECTEICITY 



[hkatdto ZFTXCn 



The flnt term la Jonle's, tlie aecond Peltier's effect. Here the 

coefficieDt of the Peltier eOect Appeals as ui electromotive farce. 

We ihall retant to this (gun. 

aiowtn^ Glomng, Melting, VolaiiliMtum, ttc. — If a wire lost 

"l^ttng. noQB of the heat generated in it, then, for tho same 

^jj^ current, the rise in iu temperature during a given time 

would Tary as its specific resistance directly, and as the 

product of its specific beat and density into the fourth 

power of its duuneter inversely. Thus, T, r, e, p, d 

denoting these qoaatities in the order named above, 

If we have a given battery of electromotive force K, 
and a circuit connected with it of resistance B, and we 
insert a wire of length I specified in other respects as 
above, the current will be ^xg ■ where 3- -^ . If the 
diamsterof the wire be given, then Soc l^ andTcc _--j, 
which is a maximum when R = S, that is, when the length 
of the wire is such that its resistance is equal to that of 
the rest of the circuit. 

Owing to our ignorance of the exact law of cooling, end 
of the manner in which the resistance and specific beat of 
most metals change at very high temperatures, it is very 
difficult to predict beforehand to what temperature a given 
current will raise a given wire. It is, as may be supposed, 
still more difficult to predict the effect of a given discharge 
from a Leydeu battery. According to Biess, the pheno- 
menon of glow in this case is complicated by concomitant 
effects of specific natural 

If we asaume TTewton's law of cooling, i.e., that the heat oivMi 
out is propoTtivital to the Bnrfoce of the wire aod to the elevatiiiQ T 
of its tempemtura over that of the eurrouadiDg medium, th«n, I 
denoting the strength of the couatant current which heata the 
wire, va have, when a constant temperature liaa been attained, 
I'— const xTi*, for wirca of aame length and material but differ- 
ent diameters. If we compare the apparent brightness of the wires, 
ty causing them to illaminate a, acrccn at b ccmatant distance off, 
and assume that the tight given out ia proportianal to Td, then, if 
two wires of diameters i^, and d, have the same apparent brightness, 
Ti^i-T^,, atldI*-HJt-It-Hf>- In other worda, the strength of 
current requisite to bring a wire of given length and material to a 

S" en brightness of glow varies directly aa its diameter. A law of 
a nature is, of course, merelj a rough approximation; Miiller 
and Zbllner, however, have made experiments which agree with it 
within certain limits. The method of Zblluer is intweetiog (see 
Wiedemann'a Oalvanimiu). 

The temperature of a glowing wire is very sensitive to eitemal 
circuniBtancca, sncb as air currents, be. These effects may lie very 
atrikingly ahown by balancing the wire in a Wheatatone s bridge 
asainst a resistance of tliiclc wire, a atrong current being seat 
through the bridge. 

The behaviour of the wire in different gases ia very remarkable. 
If a wire which is glowius in air tie Budilenly immeieed iu a jar of 
hydrogen or coal gas, the brlghtneaa will be very mncb reduced, in 
fact, in moat cases the glow will entirely disappear." This is owing 
to tha greater cooling power of hydrogen, of which evidence is i 
fumiahed \iy the ej^ierimeota of Dulong and Petit." The cooling 
power of different gaaea was shown by Grove. He arranged a 
platinum wire in a glass tube, which could be filled with dilferent 
gases. The current of the same battery was sent through the wire 
and through a voltameter. When the tulte waa filled with hydrogen 
or defiant gaa, the amount of gaa evolved in the voltameter per 
minute was 77 and 7*0 cubic inches respectively. The numbers 
for the other gases experimented on varied from 68 to B'l, They 
stood in the following order ;— CO, CO^ 0, air (2 atmoa.), N, air 
(latmos.), air (rarefied), CI Eiperiments of a similar nalure were 
made on liquids. Clausiu earrieii out a calculation of the cooling 
effect of different gaaes, and found that the experimental results 
could t>e satisfactorily accounted for.* 

When the strength of the current ia sufficiently increased, 
the wire ultimately fuses, or even volatilizes. The pheno 
menon is in general complicated. In air, for instance, the 

' RfSmnffteliclriciUit, Bd. ii. S3 567 »jq. 

' Grove, PMI. ilag., 1815, or Wied. Oaiv., Bd. i. 879. 

» Pi^gendorff, Pcgg. Ann.. \xxi., 1847. 

• Wi*i. Oidv. (t e.), or Fogg. Ann., Izzxvil., 1852. 



' wire bnms, and the oxidization once started may take % 
greater share in iHising the temperature than the curreot 
does, so that the destruction of the wire may take place 
under certain circumstances with a current, which, iiader 
other conditions, would scarcely make it glow. When di»- 
charges from a Leyden battery are used it ia very difficult, 
if not altogether impossible, to get melting unaccompanied 
with mechanical disaggregation of the wire. The reader 
who wishes for further ioformation concerning these matten, 
will find the sources sufficiently indicated in Wiedemann, 
Riess, and Mascort. 

This department of electricity is very fruitful in Pop 
popular lecture-room experiments. We shall quote one or*i?> 
two of these, and refer the reader to popular treatise* for""' 
more of the same kind. 

On asheetof thin card-board iaprickedademgo, generally what it 
understood to be a portrait of Franklin, two pieces of tinfoil an 
pasted on the ends of the card by way of electrodes, and betweeii 
these a piece of gold leaf ia laid. On the other side of the card ia 
placed a piece of white paper or silk. The whole is then tightljr 
screwed up lietween two boards. When an electric discharge ia sent 
through the gold leaf it volatilizes, sending the diaint«gntad 
particles through the holes in the card-hoard. In this way an im- 
pression of the portrait is obtained. 

If a current be caused to heat a pretty long thin platinum wtreta 
dull redness, and a portion of the wire be cooled by applying a pieea 
of ice to it, the remainder of the wira will glow much more brightly 
than before ; whereas, if a portiou be heated by a spirit-uin^ 
the reverse effect takes place. The reason id that the cturmt u 
strengthened in the one case by the decrease of the resiitance in tha 
couZai part, and weakened in the other by the increase of resistonos 
where the wire ia heated. 

When two curved metal snrfaces reat upon each other, a current 
paaaing from the one to the other encounters consideraUe resistance 
at the small area of contact. The heat developed in consequence of 
this causes the parts in the neighbourhood to expand very quickly 
when the contact ia made. This very often gives rise to rapid vibra- 
tory movements in the conductors. Tlie Trevelyan roclter* can 
be worked in thia way (see art. Heat), bella rung, he. The beat 
known experiment of the kind is Gore's railway. This consists o( 
two concentric copper hoopH, whose edges are worked reiy truly into 
the same plane. A light copper ball is placed on the rails thns 
formed, a current from two or three Groves is sent from one hoopio 
the other, aud the ball set iu motion. If the ball be very true, and 
the railway be well levelled, the energy supplied by the swelling at 
the continually changing point of contact is sufficient to keep up the 
motion, and the ball runs round aud round, emitting a crackling 
sound as it goes.* 

The Voltaic Are. — When two electrodes of volatile or Bed 
readily disintegrable material forming the poles of b power- "^ 

fnl battery (say 30 or 40 Qrova's cells) are brought into 
contact and then separated, the current coatinues to pasa 
acrusa the interval, provideid it is not too great. The con- 
ducting medium appears to be a coutiuuons supply of 
heated matter, suspended in glowing gas or vaponr. Ttaa 
phenumenoQ seems to be more akin to the subject we are 
now discussing than to the disruptive dischai^ of which 
we shall speak by-and-by. The light thus generated with 
a large battery, especially when electrodes of graphitio 
carbon are used, is brilliant in the extreme. It was thna 
that Davy first obtained the phenomenon.' With a battery 
of 2000 cells he obtained a luminous arc 4 inches in 
length, and when the carbons were placed in an exhausted 
receiver the arc could be lengthened to 7 inches. 

The fact that the electrodes must be brought in contact 
in order to start the light is quite in accordance with what 
we know of the extremely small striking distance of even 
very powerful batteries. When the contact is made, tha 
place where the electrodes touch, owing to itssmall section, ia 
intensely heated; thematter begins to volatilize, and then the 
current is kept up by the quickly increasing cloud of metallic 

» Wied. Oalv., Bd. i. % 726. 

* This motion has been attiibnted to electromagnetio action. Bach 
on explanation is quite Inadmiisibls. 

' PhU. Trant., 1821. According to Qnelelot, Curtet observed ths 
light between earbon pointj iu 1802. Wied. QiUiy., Bd. L | liS. 



60 



ELECTRICITY 



[dIBBUPTIVX DIBCflASOB. 



Theoreti- 

talcon- 

■idera- 

tiODS. 



Dtelee- 

tric 

itrength. 

Striking 
diftance. 



experiments ; Wiedemann, on the other hand, gives ela- 
borate accounts of the more modern results of De la 
Rive, Pliicker, Hittorf, and others. 

When induction is exerted across a dielectric, we may 
consider the action at any point of it in one or other of 
two ways. We may regard the resultant electromotive 
force arising from the action at a dbtance ol all the free 
electricity in the field as tending to separate the two elec- 
tricities in the molecules of the dielectric. In this view, 
we might measure the dielectric strength of the medium 
by the value of the electromotive force, when the electricity 
is on the point of passing from one molecule to the next. 
We might, on the other hand, consider, with Faraday and 
Maxwell, that the dielectric is the seat of a peculiar kind 
of stress, consisting of a tension p along the lines of force, 
and an equal pressure perpendicular to them, p being 

equal to — R* (Maxwell, voL i. § 104). We shall adopt the 

latter alternative, and when we speak of tension hencefor- 

ward it means — R'^. In this view the dielectric strength 

ox 

may be defined as that tension under which the dielectric 

just begins to give way. The reader who prefers the other 

way of looking at the matter will find no difficulty in 

translating any statement from the one language into the 

other. 

We have started by considering any point of the di- 
electric, and it is obvious that the dielectric (RupT)osed 
homogeneous) will first give way at that point which first 
reaches the limiting tension «>; just as an elastic solid 
begins to give way where the stress first reaches the 
breaking limit. It may be proved, however, that R^ can- 
not have a maximum value at any point where there is no 
free electricity, which shows us at once that the point at 
which the limiting tension is first reached must always be 
on some electrified surface, in general therefore on the sur- 
face of one of the conductors of the systeuL^ Disruptive 
discharge, thus begun at the surface of a conductor, spreads 
out into the dielectric. Its farther course is influenced by 
a variety of circumstances very hard to define in the great 
!najority of cases. 

An attempt will be made by-and-by to ^ve an idea of 
the varieties of luminous discharge that arbe in this way; 
meantime we concentrate our attention on a feature common 
to all disruptive discharges, viz., the definite limiting tension 
at which under given circumstances they begin. 

Dielectric Strength of Gases. — ^The earlier measurements 
bearing on this subject were conducted under circumstances 
which render a comparison of the results with the theory, 
as at present developed, very difficult. Harris found that 
the striking distance between two balls connected with the 
armatures of a condenser was directly proportional to the 
charge of the condenser as measured by a Lane's jar. 
Riess used a Leyden battery, and varied the number of 
jars and the charge of the battery. The balls of his spark 
micrometer ^/ere of diameters 5*7 and 4*4 lines respectively, 
while the distance between them varied from 0*5 to 2*5 
lines. Under these circumstances, he found the striking 
distance to be proportional to the charge of the battery 
directly, and to the number of jars inversely. The results 
of Harris and Riess might be summed up in the statement 
that the striking distance between two balls connected 
with the armatures of a condenser varies as the electro- 
motive force or difference of potential between the arma- 
tures. This result is purely empirical, and must not be 
extended beyond the experimental limits within which it 

^ The dielectric ia supposed to be homogeDeous. Prof. M&xwell has 
pointed oat that exceptions might occur in the case of a weak dielectric 
interposed between two strong ones, e.a.. a current of hot air passing 
through cold. 



was found. Even Riess's experiments themselves show 
that the striking distance increases more rapidly than the 
difference of the potentials. 

The experimentB of Enochenhaner* led to a similmr refolt 
Gaugain* made ezperiments of the same kind through a wider 
ranffe of striking distances, and found, in conformity wiu the refolt 
of Riess, that, with balls of 10 or 15 mm. diameter, the striking 
distance is proportional to the potential difference between the balls, 
when the distance between them lies between 2 and 5 miUimetrea. 
Beyond these limits the ratio of potential difference to atriking dis- 
tance falls off; whereas, for smaller distances, it increaaes very 
rapidly. He also found that the deviation from the law of Harris 
and Riess is more marked when unequal spheres (8 mm. and 10 
mm.) are used, and still more when a ball (8 mm. diam. used as 
+ electrode) and a disc (35 mm. diam.) were used as electrodes. 
Experiments leading to similar conclusions are cited by Maacart,^ 
who finds that, for spheres of diameter 8 to 5 centimetres, the 
striking distance for given potential difference is sensibly the same; 
whereas for plates, both the striking distance and the law of the 
whole phenomenon is different. The same experimenter examined 
the striking distances between two equal balls (8 cm. diam.) from 1 
mm. up to 150 mm. Takine the potential difference for one 
millimetre as unity, ho found for 10, 20, 40, 80, 150 mm. the 
potential differences 8*3, 11*8, 15*9, 20*5, 28-8. The deyiatioo 
from proportionality is obvious; the potential differences in fact 
tend to become constant. Wiedemann and Riihlmann, in their 
exi>eriments on the passa^ of electricity through gases (see below, 

L61), made some ezpenments on the influence of the form and 
tance of the electrodes. They used two brass'balls of 18*8 and 
2*65 mm. diameter respectively, and sent between them the dis- 
charges of a Holtz machine. The distance (8) between the nearest 
points varied from 3 to 22 '3 mm. They found that the quantity 



of electricity (y) required to produce disc 



5y toun 
haige, 



could be represented 



by the formula y = A- - and y=C-i-D8\ according as the laiger 



sphere formed the positive or negative electrode. The constants 
A, B, C, D depend on the pressure, which varied in these experi- 
ments between 25 and 60 mm. of mercury. 

In most of the experiments that have just been de-SirW. 
scribed the effect of the form of ,the electrodes and the ''**!■*" 
surrounding conductors could not be estimated theoreti-J^V 
cally. Experiments in which the theoretical conditions inm\M. 
are simple have been made by Sir Wm. Thomson.^ The 
spark was taken between two parallel plates of consider- 
able area; one of these was plane, and the other very 
slightly curved, to cause the spark to pass always at a 
definite place. The electrical distribution on the opposing 
surfaces can be found (see above, Math. Theory of Elec- 
trical Equilibrium), as if the plates were plane and of in- 
finite extent. This distance between the plates was measured 
by a micrometer, the contact reading being determined by 
observing when the electricity ceased to pass between the 
plates in the form of a spark. The potentials were 
measured in absolute electrostatic (C.G.S.) units, by means 
of Thomson's absolute electrometer (see art. Elsctbometeb). 
The limiting tension or dielectric strength is given in each 
case in grammes per centimetre, the formula for calculating 
it being 



P- 



8irx981-4flP' 



in which V represents the potential difference or electro- 
motive force between the plates, and d the distance in 
centimetres. If we take the older view of Poisson's time 
that the action of the electricity on the surface of a con- 
ductor is simply a fluid pressure, then p represents that 
pressure. 

If we could consider the air between the plates as a 
homogeneous dielectric, then, for air at a given pressure 
(and temperature?) and given state of dryness, p^ which 
measures its dielectric strength, would have a constant 
value independent of the distance between the plates, 
and Y would be proportional io d. A glance at Sir Wm. 
Thomson's^ tables shows that this is not the case. For a 



' Mascart, t. i. $ 463, or Pogg. Ann., Iriii. * Masrart ((.c). 

* t L 8 478. » Proc, R.S., 1860, or n^trint, p. «^ 

* Reprint, pp. 252» 258. 



247. 



tnSBUPTITK DIBCHABOK.] 



ELECTEICITY 



61 



distance of 00254 cm., ji = 11-290, whereas for a distance 
•lS2i, p~ '535. It appean, therefore^ that the dielectric 
■tnngth of a thin stratom of air is much greater than that 
of a thick one. It is verj difficult to understand vhy this 
should be sa " Is it possible that the air very near to 
the surface of dense bodies is condensed, bo as to become a 
better insulator; or does the potential of an electrified 
conductor differ from that of the air in contact with it, by 
a quantity having a maximoni value just before discharge, 
so that the obeerred difference of potential of the conduc- 
tors is in every case greater than the difference of potentials 
on the two sides of the stratum of airby a constant quan- 
tity equivalent to the addition of about -005 of an inch 
to the thickness of the stratum !"> It is remarkable 
that the limiting tension should be so small, somewhere 
about half a gramme per sq. cni., as compared with 
the atmospheric pressure, which is aboat 1032 gm. per 
Oq. cm. 

A series of absolute measurements of the potential re- 
quired to produce a spark between equal spheres at different 
distances has been made by Uascart. The method em- 
ployed was very ingenious.' 

rtof Efeet of Pretture, Temperature, ^e., <m the LieUctrie 

•"^ l^rengtK of Oau*. — The dielectric strength of a given gas 
depends on its pressure, or at all events on its density. 

ris. Harris, who experimented on this subject, inclosed two 
balls in a receiver which could be exhausted ta any required 
degree, and connected them with the armatures of a battery 
of jars. He found that the charge which had to be given 
to the battery in onler to produce a spark between the balls 
was proportional to the density of Uie air in the receiver, 
while it seemed to be independent of its temperature. This 
amounts to asserting that the difference of potentials re- 
quired to produce a spark between the balls is proportional 
to the density of the gas and independent of its tampera- 
ture. Since we keep the distance between the balls the 
same throughout, this statement is equivalent to saying 
that the dielectric strength of a gas varies directly as its 
density, and ioea not depend on the temperature. Uosson, 
using the method which Faraday hod employed in com- 
paring the dielectric strength of gases (vide infra) arrived 
at the same conclusion as Harris. Knochenhauer, however, 
experimenting with pressurea rauging from 3 to 27'4 inches 
of mercury, found that for a given interval the difference 
of potentials required to produce disruptive discharge was 
proportional to the pressure increased by a small constant 
quantity. 

d*j. Faraday, in the 12th and 13th series of his Experimental 
Retearehet, examines this subject ; and the reader who de- 
sires to have a clear idea of what the issues involved really 
are will do well to begin by carefully studying Faraday's 
results, and still more his views on this matter. Faraday 
directs his attention to the specific behaviour of different 
gases. 

The gss to be axsmined wis introduced into > receiver in vhich 
were smiiged two Lalls > sod I, of di&metets 0-93 in. and 3-02 in. 
resnectiTely, at a constant distance 062 in. apart. Two balls, S 
and L, of diameteiv 0*9fl in. and 1-9G in., were placed on suitable 
insulating iupporta outside the receiver. S Bud j were connected 
with au electric machine, and I aud L to earth. Ttis distance u 
between 8 and L could be raritid at will ; if it was greater than a 
ceitain value B, the sporka always passed between > and I in the 
receiver; if it was leas than a cortain value n, they always passed 
between 3 and L in the outer air. It might have been expected 
that a and B wou]d be equal, or at least very nearly so, i.t. that 
there would be one definite value of u, for wHcb the apark would 
hesitate between the alternative intervals. This is not so, however. 
Nor a|;iun is the valae of u the same when i and I are negative as 
when they are positive. The following table will illuitrato these 
points, as vtU aa the retationa of Uia different gases : — 



Gas. 



Air I U-flO 

Oxygen ; l)'41 

NiCrogeo 0-66 

Hydropn,... 0'30 

Cubonic acid. O'SS 

Olefiantgaa 0'61 

Coalgaa 0'37 

Hydrochloric acid. 0'89 



It will be seen that the different gases present consider- 
able variety, and cannot be classified in any way so as to 
connect the dielectric strength with any other physical pro- 
perty. The numbers given cannot be regarded as mecuuring 
the dielectric strength, owing to the disturbing influeacei 
which cause the inequality of a and /3. This inequality 
is not by any means small ; e.g., for air the uncertainty 
amounts to about 32 per cent. These experiments show 
very clearly that the sign of electrification of the surfaca 
at which the discharge begins has a great effect on the 
limiting tension. The discharge possee much more resdily 
from a small ball to a large one when the former is nega- 
tive than when it is positive. Faraday made a variety of 
experiments to elucidate this point, and he was driven to 
the conclusion " that, when two eqaal small conductiug 
surfaces equally placed in air are electrified, the one pou- p 
lively the other negatively, that which is negative can ai 
discharge to the air at a tension a little lower than that jP 
required for the positive surface, and that, when discharge ^ 
does take place, much more passes at eatji time from the 
positive than from the negative surface." 

The inequality of a and p may be due to various causes, 
among which may be mentioned the charging of the glass 
of die receiver, dust, Ac, in the air, heating of the air, 
and the presence of finely divided metal dispersed by pre- 
ceding sparks. The last of these causes would account to 
a considerable extent for the fact that the sparks show a 
tendency to persist in a path once opened, and that the 
interval j9 ~ a is less for the negative spark, which starts 
at a smaller limiting tension, and may therefore be sup- 
posed to produce less mechanical effect. 

Wiedemann and Rtihlmonn have recently taken up this H 
subject in a research which has already been alluded to.' '" 

The gas and the spark terminals were inclosed in a eylindiical r, 
metal receiver with ronnded ends. A small icindow allowed tbe ^ 
light from the spark (o fall on a rotating laiiror fixed on the aiis of 
a Holli machine, which furnished the electricity. The images of the 
succcaidve sparks were observed by means of a heliometer. One-half 
of the divided object-glass was moved until one of the images of one 
discharge coincided with one of the images of the next ; then ■ 
similar ^incidence was brought about by displacing the halT-lens 
in the oppofdte direction. Tbe difleience (y) of the two readinip 
on the micrometer of tbe heliometer measurea the rotation of the 
disc of the Holti machine between the two aparks. Preliminary 
experiments showed that the amount of electricity famished by the 
machine while the disc moves through a giren angle is indepeudent 
of the angular velocity of the disc. It varies from day to day, 
however, according to the quantity of moisture io the air and the 
arrangement of the machine ; but, on the principle just laid donn, 
correction can easQy Dc made by takiug tbe reading each day at a 
ter through which tbe current of the m - — 



S,iw, 



therefore, that y is proportiuuat to the quantity of elec< 
different oaya c 



ricity which poiaea at each diichsrge through the gas, and by 
means of a galvanometer observatioQS on diffe 

It was found that at the lowest pressures worked with 
{'5 to '25 mm. of mercury) the discharge of the Uoltz 
machine was still discontinuous ; and that in all the ex- 
periments the tension at the electrodes was such that the 
discharge was independent of the nature of the metal, — in 



Oa/c, iL 2, 



G2 



ELECTRICITY 



[diseufhys dischabob. 



High 
pres- 
■nres. 



Mlnimam 
■irength. 



Strength 
of va- 
cuoin. 



other words, that the disintegration of the electrode played 
no esseutial part in the discharge. 

The quantity of electricity required to effect a discharge, 
other things being equal, increases with increasing pressure. 
This increase is at first rapid, then slower, and at high 
pressures it is nearly proportional to the increase of pressure. 
It was found that y could be expressed with sufficient accu- 
racy in terms of the pressure p by the empirical formula, 
y = A + B/> - C/^, in which the constants A, B, C depend on 
the size and insulation of the electrodes, their distance 
apart, and so on. 

They arrange the gases in the following order of dielectric 
strength : — hydrogen, oxygen, carbonic acid, air, nitrogen. 
It is not a little remarkable that this is the order given by 
Faraday in the second column (the best) of the results we 
quoted above. 

They find, in agreement with Faraday, that a greater 
quantity of electricity is required to bring two unequal 
spheres to the discharging point when the small one is 
positive than when it is negative. When two equal spheres 
are used, the value of y is least when both are insulated, 
greater when the positive sphere is uninsulated, and very 
much greater when the negative one is uninsulated. 

All this is in accordance with theory, provided we assume with 
Faraday that the limiting tension is greater at potdtive than at nega- 
tive surfaces. For example, suppose the surface densities correspon- 
ding to the limiting positive and negative tensions to be P and N 
(P^N), and consider the case of two eqoal spheres of radios a, at so 

great a distance e apart that ( - j may be neglected, then by taking 

three consecutive images the reader will easily find that the charges 
which most be given to either ball in the case where both spheres 
are insulated ana equally charged, and to the negative ball in the 
case where the positive ball is uninsulated, and to the positive ball 

when the negative ball is uninsulated, must befl-8^]4va*N, 

4»a'N , 4ira'P , respectively, in order to produce discharge. The 
dischar^ begins at the ne^tive ball in the first two cases, and at 
the positive ball in the third, and the quantities are obviously in 
ascending order of magnitude when P is >-N. 

The dielectric strength goes on increasing when the 
pressure is raised above the atmospheric pressure. Cailletet^ 
found that a powerful induction coil worked by eight large 
Bunsen cells was powerless to effect discharges across \ mm. 
of dry gas at a pressure of 40 or 50 atmospheres. 

On the other hand, however, the dielectric strength does 

not diminish indefinitely as the pressure decreases, but 

reaches a minimum. 

Morren and De la Rive' have sought to determine this minimTiTn 
dielectric strength by measuring by means of a galvanometer the 
mean intensity of the current sent through the gas by an induc- 
torium so arranged that only the direct induction current passes ; 
they thus obtain what they call a Tninimnm rtsifiancit. Morren 
gives the pressures corresponding to this minimum for various gases; 
they lie between 0*1 and 3*0 mm. It may be questioned whether 
any very definite meaning can be attached to results of this kind; 
for the discharge is discontinuous, and resistance in the proper sense 
of the tenu cannot be spoken of. 

It is clear, however, that a minimum dielectric strength 

must exbt ; for, if we go on improving our vacuum, we 

find that our ordinary machinery fails to send electricity 

through any considerable length of the exhausted space. ' 

Morgan* seems to have been the first to discover that the electric 
s{>ark would not pass in a vacuum. Having carefully boiled the 
mercury in a barometer tube, so as to remove the last traces of 
moisture, he found that the inductive discharge caused by electri- 
fying a piece of tinfoil on the outside of the tube would no longer 
pass to the mercury, and cause the luminous phenomena usnidly 
seen under such circumstances. Masson repeated this experiment 
in a more satisfactory form. Gassiot^ greatly improved the exhaus- 
tion of vacuum tubes by filling them with CO,, pumping out as 
usual, and then absorbing the residual gas by fusing a piece of 
KHO previously inserted into the tube. He constructed tubes in 

^ Mascart, t. L S 187 
• PhU. Ttans,, 178& 



* Wiedemann Bd. iL § 952 

* PhiL Trans., 1869. 



this way which had sufficient dielectric strength to insulate the pole 
of his fpreai battery of more than 3500 Zn. Aq. Cu. cells. Uittoif 
and Geissler* have constructed vacuum tubes (by pumping with a 
Geissler's pump, and heating the whole to 400* to 500* C.) in which 
the opposition to the discharge of an interval of 4 nim. between 
two platinum electrodes was greater than that offered by 15 or 20 
centimetres of ordinary air. 

Different Forms of the Discharge in Gases, — ^We have said Ptojb 
that the subsequent progress of the disruptive discharge ^'^ 
when once begun is influenced by a great variety of circom- ^|^ 
stances. The beginning of the discharge evolves heat, chaqi 
which rarefies the neighbouring air, and therefore weakens 
its dielectric strength. Owing to this cause the discharge 
once started tendis to go on. Again, if any considerable 
quantity of electricity escapes into the ruptured dielectric 
at the first burst, this relieves the tension at the surface of 
the conductor. On the other hand, the progress of part of 
the electricity towards the opposing conductor raises the 
tension at the surface of the latter, so that disruptive dis- 
charge is provoked or helped there. If the initial tension 
is considerable, or the quantity of electricity which passes 
to begin with very great, glowing metal particles are shot 
forth into the dielectric, causing a reduction of its strength, 
which will be very different in different directions. Motions 
of the air play a great if not a preponderating part in many 
forms of the discharge. The electrification, dba, of the 
walls of the tube, and the f urm of the electrodes and of the 
tube, both in the neighbourhood of the electrodes and at a 
distance from them, are as important in their influence on 
the continuance of the discharge as they are on its start 
And, last but not least, much depends on the way the 
electricity which produces the discharge is furnished, — on 
the nature of the electromotor, in short Although we liave 
not yet exhausted the influencing conditions, we have pro- 
bably said enough to convince the reader that little aid is 
to be hoped for in this matter from considerations a priori. 
There is a great deficiency even in proximate principles to 
guide us in the maze of experimental detail; and although 
most of the experiments are beautiful beyond all conception, 
yet the mere narration would scarcely interest the reader. 
Our description of the department will, therefore, consist 
simply in going round the boundary. 

The luminous appearances may be roughly classed under 
the forms of spark, brush, glow and convective discharge, 
and dark discharge. 

At the ordinary atmospheric pressure the disruptive dis- Spul 
charge between two conductors at a moderate distance apart 
takes place in the form of a brilliant sharply-bounded streak 
of light, whose apparent breadth is in general smalL For 
small distances the spark is straight, and has the appearance 
of being thicker, or at least more brilliant, at the ends than 
in the middle. Y/lien the distance is considerably increased 
the spark assumes the characteristic zig-zag form seen in 
forked lightning. It seems occasionally to be absolutely 
broken by perfectly dark spaces. The duration of the dis- 
charge in this form, more especially when the resistance of 
the discharging circuit is very small, as tested by a rotat- 
ing mirror, appears to be exceedingly short 

We have taken photographs of the sparks of a Holtz*8 machine by 
simply moving the camera containing the sensitized plate vertically 
upwards past the electrodes of the machine. The result is a colonm 
of perfect photographs, ouite unblurred by the jarring, &c., ol the 
camera stand. Again, if a disc painted with white and Dlack 
sectors be caused to rotate very rapidly, it appears in ordinary light 
to have a uniform grey colour; but when it is viewed by the light 
of an electric spark the sectors ai-c seen exactly as if the disc were 
at rest, which proves that the illumination lasts for a very short 
time. Masson founded on this experiment a beautiful method 
for measuring the intensity of the lignt given out by the spark. A 
description of his apparatus, with an account of his results, will be 
found in Mascart. 

The colour of the spark in air is bluish,^ but at the same 
» Pogg, Ann., 1869. • Faraday, Rtp. JUs,, 1422. 



XTPTIYB DIBOHJLBOB.] 



ELECTRICITY 



63 



time its great brilliancy gives an impression of whitenesa 
In nitrogen the appearance is much as in air, only the 
colour tends more to bluish purple, and the spark is more 
sonorous. In oxygen the spark is whiter and less brilliant 
than in air; in hydrogen crimson-coloured; in carbonic 
acid greenish ; in hydrochloric acid white, and never broken 
by dark parts ; in coal gas green or red, with occasional 
Suk parts. If the spark be carefully examined, especially 
when the pressure is greater than an atmosphere, it will be 
leeo that the central bright streak is surrounded by an 
envelope, of somewhat nebulous form, and of a lavender- 
blue colour. This envelope tends to spread over the nega- 
tive electrode, where it is moie conspicuous as compared 
with the central streak than elsewhere. This envelope ap- 
pears to be due to the glowing metal particles torn from 
the electrodes. It has, unlike the centnd streak, a sensible 
duration, on account of which it happens in many cases 
that a much greater quantity of electricity passes through 
it than through the infinitely more brilliant but less endur- 
ing part of the discharge. The envelope can be actually 
separated from the streak by a current of air properly 
directed, or by the action of a magnet (vide infray p. 

When the discharge in air at the atmospheric pressure 
takes place between a saliejU but not pointed part of one 
conductor and another conductor of considerable surface 
{e,g. between one sphere 2 cm. diameter and another 13 
cm. diameter), the luminous appearance very often takes a 
characteristic form, which has been called the brush dis- 
charge. The name is to a considerable extent descriptive 
of the phenomenon; if the word broom had been applied it 
would have been even more appropriate, and a rough idea 
of the variety of forms the brush may assume will be 
obtained by thinking of the various forms of the domestic 
vticlein question. At the surface of the smaller conductor 
appears a short, straight, luminous stem differing in appear- 
ance very little except in brightness from a sparh From 
this radiate a series of twig-like branches of much inferior 
brilliancy, having *a purplish- violet colour. These sub- 
divide in many cases into still smaller ramifications, and are 
ultimately lost in the medium. When the large conductor 
is either altogether absent or very distant, the general ten- 
dency of the branches is to spread outwards more and more 
in all directions ; but when the large conductor is brought 
nearer, the branches have a tendency to bend down towards 
it, so that the whole assumes an ovoid shape. The brush is 
generally accompanied by a crackling or hissing sound, or 
even a musical note. On approaching the hand or a con- 
ductor of extended surface, the pitch of this sound rises con- 
siderably. This at once suggests that the brush is an inter- 
mittent phenomenon. That this really is so was clearly 
proved by Wheatstone in one of the earlier applications of 
his rotating mirror.^ Wheatstone saw in his mirror not one 
image of the brush, but several arranged in succession at 
regular intervals. Each of these images corresponds to a 
single discharge, and each appears less complicated than the 
brush as viewed by the unaided eye, which is, in reality, a 
superposition of a considerable number of brushes, the 
number depending on the time taken by a light impression 
to fade on the retina. At the same time each individual 
image is a little drawn out in the direction of motion of the 
mirror, which shows that the brush has a sensible duration. 
Faraday speculates very acutely concerning the nature of 
the brush discharge (see Exp. Res.y 1425 sqq.). He finds 
that, although it is generally accompanied by a current of 
air, yet it b not always or necessarily so. He also care- 
fuUy illustrates the difference between the positive and 
native brush. If we have a small ball on the end of a 

» PhiL Tram.. 1831, &c. 



wire projecting freely into the air, the positive brushes' ob- 
tained from it are much lai^ger and finer than the negative 
brushes so obtained. Again, if we charge a large metal 
ball positively, and bring an uninsulated metal point up to 
it, a star appears on the point, which gets brighter and 
brighter as the point approaches the sphere, but the 
form does not change until the distance is very small 
If the sphere be chsu-ged negatively, the star appears as 
before when the distance is considerable, but at a mode- 
rate distance (1 to 2 inches) a brush forms, and when the 
distance is still farther reduced a spark passes. It seems, 
therefore, that the negative discharge keeps its form un- 
changed under considerable variety of influencing circum- 
stances, whereas the form of the positive discharge is more 
readily affected. The explanation of these differences he 
finds in the fact, which he established by experiments already 
alluded to, that the limiting tension is smaller at positive 
than at negative surfaces; so that, cctteris parous, the 
negative discharge occurs oftener than the positive discharge; 
but, on the other hand, when the latter does occur, more 
electricity passes. This, no doubt, accounts for the lower 
pitch of the sound of the negative brush, and the greater 
extent and brilliancy of the positive one. Faraday found 
great differences in the character of the brush in different 
gases; in none apparently does it reach the brilliancy 
attained in air or nitrogen. He also observed that rarefac- 
tion up to a certain point favoured the production of 
brushes. 

When discharge takes place from the rounded end of a Glow, 
wire projecting freely into the air, the brush is very often 
replaced by a quiet phosphorescent glow, which covers a 
greater or less extent of the end of the wire. The noise 
which accompanies the brush is entirely absent in this form 
of the discharge, and the means by which the brush can be 
analysed into a series of successive discharges give no cor- 
responding result for the glow. In the rot iting mirror it 
simply stretches out into a uniform band of light The glow 
is therefore either a continuous discharge or an intermittent 
discharge of incomparably shorter period than the brush. 
Diminishing the discharging surfaces favours the produc- 
tion of glow.^ Increase of power in the electric macliine 
which is fumishing the electricity has a similar effect 
Rarefaction of the air has also a great effect in facilitating 
the production of glow, especially in the case of negative 
glow, which is extremely hard to produce io air at common 
pressures. In Faraday's opinion, the star which is ob- 
tained with a positive sharp point is a positive glow ; but 
he thinks it not improbable that the negative star is not 
a negative glow, but a small negative brush. The glow is 
invariably associated with a current of air to or from 
(generally both) the glowing conductor. Everything that 
favours this air-current increases the glow ; e.g., a brush 
may sometimes be converted into a glow by properly 
directing an air-current near it Again, everything that 
prevents or retards the formation of an air-current has a 
similar effect on the glow : a glow can be converted into 
a brush in this way. Lastly, everything which tends to 
prevent abrupt variation of the tension favours the glow, 
and everything having an opposite tendency is destructive 
of it Faraday concludes, Uierefore, that the glow is due 
to a gradual discharge by convection, in which the agents 
are the particles of the gas. The order of the appearance 
of spark, brush, and glow at positive and negative surfaces 
is, in general, the same; but the gradation is different 
Positive spark does not pass into brush so soon as negative 
spark does ; but, on the other hand, positive brush turns 
to glow long before negative brush. 



* By positive brush, of course, is metnt brush emanating from a 
positifely chai^sced surface. ' £xp. Res., 1627. 



64 



E L B C T-K I C I T T 



[dissdptitb dischab^ 



ConT*ii- Intimatelf connected with the glow U the conrectire 
iivsdlt- discharge, lif indeed they are not degrees of the same 
chugp. phenomenon. "The electric glow is produced by the 
constant passage of electricity through a small portion 
of ait in which the tension is very high, so as to charge 
the surronndiug particles of air which are continaatly 
swept off by the electric wind, which is an essential part 
of die phenomenon."' Now there seems little reason to 
doubt that at lower tensions^ dischaige of this kind may 
occur withont the lamiuouB phenomenon at the surface of 
the conductor. If this be so, then the cunrective dis- 
charge is only a different degree of the glow discharge. 



ueiglibourbaod of B&IieQt tnglei tban eliewhere. Such electrical 
atmotpkerei are ofUii a Boarce of great incoaTanieiice in the labora- 
tory and lectore-room when delicate electrical eEpeiitUBntt are in 
progress. 

A curious little izutramect, called tbe electrical toamiqnet or 
windmill, depends Tor ita actioa on the electrical wind which 
accompanies conrectiTe discharge. A small rectangular cross, 
with eiiQal arms, is made of light wire ; the extremities of tbe arms 
are bent through a ru^t angle in the iilane of the cross, so as to 
point all one way. The little cross thus made U poised, like a 
compass needle, OQ a vertica] wire connected with an electri&ed 
conductor. Convective discharge takes place at the points, giriug 
rise to an electrical wind, the reaction of which causes the little 
machine to revolre with great rapidity. If the experiment be con- 
ducted in the dark, a glow tUDally appears on the rerolving points. 
The experiment auo sncceeds when the cross is immertea in a 
non-condncting liquid. 
Dark We have already allndod to the dark spaces that some- 

bterTsL times appear in the spaik in gas at the atmospheric pres- 
sure. Faraday ohserred that a phenomenon of this kind 
was very common in coal gas. When the discharge takes 
place in highly rarefied gas, a dark space of this kind 
almost always separates Uie positive from the negative 
light, ita situation having a certain degree of fixity with 
respect to the negative, but not to the positive electrode. 
It is very difBcult to form an idea of the exact nature of 
the discharge which takes place in this space. Discharge 
there undoubtedly is of some kind; and pending (urther 
investigation, Faraday called it the dark discharge. The 
fact that its real nature is still undiscovered amply justifies 
the separate name. Faraday found that it occurred in dis- 
cfaai^ea that pass almost instantaneously, and concluded that 
it could hardly be due to convection of the ordinary kind, 
which requires time. De la Kive and Hittorf have made out 
many peculiarities connected with its appearance in vacuum 
tubes, the phenomena iu which we now attempt briefly to 
describe, 

nreSed One of the most common used to be the electric egg, which is 
simply an oval glass vessel furnished with two small metal spheres 
for electrodes; the stems which cany these electrodes pass air-tight 
through tubes cemented to tbe ends of the vessel ; the stem which 
supports the whole is perforated and fitted with a stop-cock, so 
that the apparatus can he exhausted to tny required extent and 
then temporurilj dostd. The commoneat of all iustmments of this 
kind no«-a-daya is the Geissler tube This is sitciply a glaee tube, 
into which are fused two electrodes of platinom or other metal ; a 
capillary tube allows tbe apparatus to be connected with an air- 
poiop, and exhausted ; when this is done, the capillary tuba is 
sealed np bj means o! a spirit-lamp. A very common form of 
such tube is the spectrum tube [see art. Lioarj, coosiitiiig of two 
wider parts, connected by a capillary part, iu whicn the light of 
thedischaive is much more Intense ttum elMwhere. Complicaled 
tnbea oF all kinds have also been constructed as electric toys. 

The reader must not forget that the form of the tube exercises 
a great influence on the phenomena, whether at the positive or 
nt^tire electrode. In the summary description that fullows the 

' Maxwell, KUeiTicUy and itagnetitn, i. | G5. 
* The reader will sot forget the exact sause in which we use the 
word tension. Qt conne, low tension doas not mean low potontiaL 



electric egg i» referred to, unless it is otherwise stated. We hr. 
ther >ssame that the electromotor used gives currents in one direc- 
tion only. A Holti machine wonld satisfy this condition, withla 
certun limits at least. 

When the gas is rarefied to a considerable extan^ tbe 
spark loses its sharp outline, becomes intersperBed with 
nebulous portions, and by-and-by loses its characteriBtie 
form altogether. As the rarefaction goes on, the discharge 
ceases to reach from the positive to the negative electrode. 
The latter now displajrs a patch of lavenderblue lig^t, 
separated from the positive light by a dark interval, tbe 
length of which depends on the distance between the elec- 
trodes. In certain cases the positive light tenninates id a 
cup-shaped depression, whose concavity is turned towards 
the negative electrode. As the rarefaction is still further 
increased, the positive light tends more and more to fill 
the tube, although in general it recedes from the nega- 
tive electrode, over which, on tbe other hand, the heantt 
ful lavender glow spreads more and more, exhibiting M 
the same time a growing tendency to fill a limited space 
mrrouTtding the electrode. At a still higher degree of 
rarefaction, the positive light, which now occupies a ctm- 
siderable space, and takes a shape more or less correspond- 
ing to that of the inclosing vessel, is divided transversely 
into a number of cup-shaped strife, separated from each 
other by darker intervals. These stris vary in form and 
appearance considerably, according to circumstances. In 
the neigbbonrbood of the positive electrode, their sxm- 
cavity is turned towards tbe positive electrode; bnt 
towards tbe other end of the positive light, the concavity 
may be turned the other way, especially in the electric 
egg. The positive light, in vacuum tubes, shows there- 
fore tbe same remarkable variability, and the negative 
light the same measure of stability that Faraday remarked 
in gas at ordinary pressures. The colour of tlie positive 
light varies very much in different gases ; in nitrogen and 
air its rosy-red colour contrasts very sharply with the bine 
oC the negative light. The negative light is remarkabU 
for its power of producing fluorescence. It is very depen- 
dent as to its extent on the form and size of the uncovered 
surface of the electrode ; anythiag placed on the electrode 
cuts it off sharply, as if the light were projected from the 
electrode and stopped by the obstacle. Disintegration of 
the negative electrode also goes ou very rapidly, so that; 
after a vacuum tube has been used for some time the 
glass all round the negative electrode is blackened, 
browned, kc, as the case may he, with a deposit of finely 
divided metal The quantity as welt as the quality of 
this deposit depends very much ou the nature of the 
metal ; it is smallest with aluminium, which is on that 
account much used for electrode terminals. The negative 
light occasionally shows one, two, or even three stratifica- 
tions; but in this respect it never equals the positive 
light. When tbe rarefaction ia carritui to the utmost, 
both positive and negative lights fall off greatly in splen- 
dour. The negative light contracts more and more in 
upon the electrode, and confioes itself even there to a 
small patch near the end, showing, however, a tendency to 
pass along the axis of the tube towards the positive elec- 
trode. Tbe positive light, on the other hand, gradually 
draws inwards, till at last it is only a star on the end of 
the electrode, which now disintegrates, owing to the great 
tension. 

Tbe temperature at the two electrodes ia, in general, very Ti 
different The true explanation of this differenca has not i* 
been made out, although it is doubtless connected with the ^ 
equally unexplained differences in the light phenomena. 
A general rule has been laid down, that the temperatnie 
of the negatJTe electrode ia always higher when the dis- 
cbarge takes place through the go* alone, and the tempera- 



BIBRUFnyS DISCHABOB.] 



ELECTRICITY 



65 



tore of the positive electrode higher when the discharges 
pass mainly through particles of disintegrated metal. The 
former case is commoner in vacunm tubes, where the 
negative electrode may get white hot, and even melt, while 
the positive electrode remains quite dark. The latter case 
is exemplified in the voltaic arc, in which great disinte- 
gration of the positive electrode is accompanied by a 
higher temperature there. Attempts have been made to 
investigate the temperature in different parts of the tube, 
and it seems to have been made out that the temperature 
is lower in the dark intervals than elsewhere. 

When the electromotor is an induction coil, which fur- 

nishes discharges alternately in opposite directions, there 
will be a mixture of positive and negative light at each 
electrode, unless the maximum tension corresponding to 

B- the inverse discharge be so small that the direct discharge 
m. alone can break through. If, however, the tube be 
examined by means of a rotating mirror, or if it be itself 
fastened to a rotating arm, the images of the different 
discharges will be separated, and it will be seen that the 
appearances at each electrode alternate. 
^ Again, when a Leyden jar is discharged through a 

[an vacuum tube, the appearances at the two electrodes are 
often very much alike, particularly when the resistance of 
the discharging circuit is very small. When the resist- 
ance is increased by introducing a column of water or 
lengths of wetted string, the appearances are similar to 
those indicated in our summary description. The reason 
of this is fully explained by the observations of Feddersen. 
He examined the spark of a Leyden jar by means of a 
rotating concave mirror. The machine which drove the 
mirror had a contact-maker, which brought on the dis- 
charge when the mirror was at a definite position ; the 
image of the spark was thus thrown by the mirror on a 
piece of ground glass or a photographic plate, properly 
placed to receive it He found that the discharge assumed 
three distinct characters as the resistance of the discharging 
circuit was gradually decreased. 

ler* 1. The discharfe was iTUermiUent, that is to say, consisted of a 

1 series of partial discharges all in the same direction, following each 
[ts. other at more or less irregular intervals. 

2. When the resistance was reduced to a certain extent, the dis- 
charge became continuous. The image of the spark on the plate 
bad then the form of an initial vertical strip, with two horizontal 
strips extending from each end, and ^^radually thinning off to a point 
The vertical stnp indicates a single initial spark, and the horizontid 
bands the finite duration of the light from the glowing metal par- 
ticles, &c, near the electrodes. 

8. When the resistance is venr small, the discharge is oscillatory, 
i,e,f consists of a succession of dischaiges alternately in opposite 
directions. These oscillations are due to the self-induction of the 
dischamng circuit ; we shall examine the matter more carefully 
under Electromagnetic Induction. 

It is obvious that when the discharge is either intermittent or 
continuous, the luminous phenomena will be of the normal form 
sketched above, hut when the discharge is oscillatory there will be 
a mixture of positive and negative appearances at each electrode, 
the independent existence of which cannot be detected by the 
unaided eye. 

lliis is the place to remark that it is rarely that the discharge is 
of the simple form (2), i,e., consists of a single continuous discharge; 
in bv far the great majori^ of caaes it consists of a series of partial 
discharges. With the inductorium, both varieties (1) and (3) may 
occur according to the length of the air space, the resistance of the 
whole secondary circuit, and so on. A number of very beautiful 
experiments have been made to illustrate these principles, which it 
would take us beyond our limits to describe. Good summaries of 
the results of Felici, Cazin and Lucas, Donders and Nyland, Ogden 
Rood and Alf. Mayer, will be found in Mascart and Wiedemann. 
Recent researches of a very important character have been made by 
Wttllner* and Spottiswocide' on the discharge in vacuum tubes. 
They employ the rotating mirror. It would be premature to attempt 
to sum up or criticise their results, suffice it to sav that they show 
an amount of a^pieement which augurs well for tne future of this 
blanch of electrical science. The striaa seem, according to them, 

» Pogg. Ann., «* Jttbelbd.,»» 1874. « Proc, R. S., 1875-6, 7. 



to play a more essential part in the phenomenon than was perhaps 
previously expected. Spottiswoodo, in fact, seems to incline to the 
view that all discharges naving a dark interval are really stratified, 
although, owing to their rapid motion, the strata may not be distin* 
guishable by the eye alone. 

In connection with this subject it may be well to mention 
the early experiments of Wheatstone,^ to determine the so- 
called velocity of electricity in conducting circuits. Six 
balls, 1, 2, 3, 4, 5, 6, were arranged in a straight line on a 
board ; 2 and 5 were connected with the coatings of a 
charged Leyden jar ; discharge passed by spark from 2 to 
1, then through a large metallic resistance to 3, thence by 
spark to 4, then through a large metallic resistance to 6, 
and thence by spark to 5. It was found, as Feddersen 
observed later, that the introduction of the metallic resist- 
ance increased the duration of the sparks at all the inter- 
vals, so that the images in the mirror were lines of small 
length ; but, in addition, the spark between 3 and 4 began 
a little later than the sparks at 1, 2 and 5, 6, which were 
simultaneous. From this the velocity of electricity has 
been calculated, by taking the interval * between the sparks 
to be the time which the electricity takes to travel through the 
metal unre bettveen the intervals. Faraday long ago pointed 
out that this interval depends on the capacity of the wire, 
and may vary very much according to circumstances. It is 
very great in submarine telegraph wires for instance (vide 
supra, p. 36). Accordingly, the values of the so-called 
velocity of electricity, which have been found by different 
observers, differ extremely. 

The sketch we have just given of the disruptive discharge 
in rarefied gases must be regarded as the merest outline. 
There are many points of great importance to which we 
have not even alluded. Hittorf s investigation on what 
has been called the "resistance*' of different parts of a 
vacuum tube during the discharge has not been mentioned, 
although it led to results of much interest, which must 
come to be of great importance when the clue to an explana- 
tion of the whole phenomena has been found. The reader 
who desires to study the matter will find in Wiedemann an 
excellent account of Hittorf's work, with references to the 
original sources. We have not so much as raised the deli- 
cate and difi&cult questions concerning the spectroscopic 
characteristics of the discharge. A good part of this sub- 
ject belongs indeed more properly to the science of Light. 

Miscellaneous Effects, chiefly Mechanical. — Owing to the 

heat suddenly developed by the electric spark, and perhaps 

to a specific mechanical effect as well, there is a sudden 

dispersion in all directions of the particles of the dielectric. 

This commotion may be shown very well by means of Kin- 

nersley's older fonu of the thermo-electrometer ; or Gauss's 

instrument may bo used if we replace the thin wire by a 

couple of spark terminals. When the spark passes, the 

liquid in the stem sinks suddenly through a considerable 

distance, even if the spark be of no great length (2 to 3 

mm.). ^ 

Yerv curious effects are obtained when an electric spark is repeated 
several times at a little distance above a plate strewed with finely 
powdered chalk. After a time the chalk is seen to be divided by a 
network of fine lines, resembling the markings on shagreen. If a 
plate of glass be covered with powdered charcoal, and the spark 
passed through the powder, it arranges itself in a series of stris 
closely resembling those seen in a vacuum tube. 

The power of the spark to induce chemical combination 
(in particular, combustion) is due no doubt mainly to its 
high temperature. 

The discharge through non-conducting liquids may take 
place in the form of spark or brush. The brush, however, 
is poor compared with that obtained in air, and is very hard 

» PhU. Trans., 1834. 

* A better statement would be " the time that elapses before sufficient 
electricity has reached 3 and 4 to raise the tension at their nearest 
points to the disruptive limit," 

vm — 9 



Wheat- 
stone's 
experi- 
ments. 
Velocity 
of el^- 
tricity. 



Kinners- 
ley's ex- 
periment 



8trin 
from 
con- 
cussion. 



DIs. 

charge in 
fluids. 



ELECTBICITY 



to get When the eparfc passes, presanre is aaddenly trana- 
mitted througb the fluid in all directions, and if it be in- 
closed in a tube tiie tabs is generally broken, even Trben 
the spark is hy no means long. When the surface of the 
liquid is free, a considerable portion is usually projected 
into the air. The convective discharge is reiy marked in 
liquids. If two small balls connected with the electrodes 
of a Holtz'a mschiae in action be dipped in paraffin oil at 
a small distance apart, the whole liquid b thrown into 
violent motion by the convection currents, runs up the vires 
which lead to the balls, and spouts off in little jets. 

Then is kIbo a distinct he&ping np of tlie liqmd betrween ths 
balls, and it one of them be f^radiiLllT witbdrnvn from tbe liquid, 
for a MDtinietre or so it rauet > comma after it, whicb adberea 
nntil tbe mochiae is stopped. It is rer; probiljle that other effects 
due to the altenitioQ of the apparent surface tension, owin^ to the 
dilTerence of electrical stress In the air and oil, are preaent in these 
phenomena, but this is baidl; the place to discuss the matter. 

The electric discharge passes with great facility through 
card-board and other bodies of loose texture. In all pro- 
bability the air m such cases has quite as much t« do with 
the resulting effects as the solid body. 
Lollln's ^ ciuioUB experiment of this kind ia ortcn made. Two points 
aip«rl- are airansed so as to touch the opposite sides of a piece of card-board, 
neat. Ifthe pointa be opposite each other, the diachar;ge passes straight 
through, leaving m the case of small charges a tinjr hols with burnt 
edges. If, however, the poiots be not oppoeite each other, tJie 
perforation occurs in the neighbourhood of the neEatire point. The 
pecoliaritj is no doubt connected with those diSecencea between 
positive and nisative discharges in air which we have several 
tantes noticed above. In fact, it is found that ia an eihansled 
receiver the card ii pierced at a spot very nearly eqaidistant from 
tbe two points. 
Dii. In other cases the main part of the dielectric strength 

clurgein depends on the solid materiid. Tbe power of such bodies 
solids. (4) sustain the electrical tension is often very considerable. 
Yet there is a limit at which they give way. A thickness 
of 6 centimetres of glass has b«en pierced by meana of 
a powerful induction coiL 

In such experiments special preeatttious have to be taken to 
prevent the spark from gliding over the surface of the glass instead 
of going throuEh ; this is managed in some cases by embedding the 
glass alonz with the terminals of the coil iu an electrical cement of 
considerable insulating power; in ordinary experiments, however, 
it is in general saScient to placa a drop of olire oil ronnd one of 
tbe terminals where it abuts on the slaaa. The appearance of the 
perfontioiis depends considerably on Uie qnantity of electricity that 
paases in the discliarge. In some case* the gUaa cracks or even 
breaks in pieces. In some large blocks we have seen a peifontioD 
in the form of several independent tbreade, each of which had a 
wrt of beaded structure, which may poasiUr be in some way ana- 
logoaf to the itratificatioos in vacaiiin tubes. 
Sorfaca Diteharge along the Surface of a Body, Dtat FiffHret, 
elsctri- ami Dust Imaget. — The class of phenomena referred to 
flcatioD. under this head are remarkable for the methods by which 
they are usually demonstrated. They were at one time 
much studied on account of the light they were supposed 
to throw on the nature of the so-called electric fluid or 
fluids. Though no longer regarded in this light, they have 
reference to on extremely important and comparatively 
little studied subject, viz., the distribution of electricity 
over the surface «[ non-conductors. It is easy to see that 
the demonstration of surface electrification on insulators is 
beset with difficulties of a pecnliar kind. A very con- 
venient method is to project on the surface a powder elec- 
trified in a known way ; this powder clings to the parts 
oppositely electrified to itself, and avoids those similarly 
electrified, so that the state of the surface is seen at once. 
Lycopodium seed and powdered resin have been used in 
this way ; they are sifted through linen cloth, the lyco- 
podium becoming thereby weakly positive, and the 
powdered resin strongly negative. If the lycopodium be 
OBod, it covers both positive and negatively electrified 
patches, only tbe latter mnre thickly than the former. 



The powdered resin, on tlie other hand, covers tbe poaitivfl 
and avoids the negative regions. The meet effectiv« 
powder, however, is a mixture of flowers c^ snlphnr* ud 
red lead. In the process of sifting, the red leaid powder 
becomes positively and the sulphur negatively electrified, 
and the powdeia separate themselves. The snl^^nr 
colours positive regions yellow, and the red lead coloois 
negative, regions kA. The result is vety striking ; and 
the test is found to be very delicate. 

The dust figures of Lichtenberg are one of the beat Lickh 
known instances of tbe kind of experiment indicated ho^t 
above. A sharp-pointed needle is placed perpendicular to ^^^ 
a non-conducting plate, with its point very near to or in 
contact with the plate, A Leyden jar is discharged into tbe 
needle, and the plate is then tested with the powder. If 
the electricity communicated to the needle was positive, 
a widely extending .patch is seen on tbe plate, oonajstiag 
of a dense nucleus, from which branches radiate in sll 
directions. If negative electricity was used, tbe patch u 
much smaller and has a sharp circular bonndai; entiiely 
devoid of branches. This difierence between tbe posttive 
and negative figures seems to depend on the preaeace of 
the air ; for the difference tends to disappear when tbe 
experiment is conducted in vacuo. Riess explains it by 
the negative electrification of tbe plat« caused by the fric- 
tion of the water vaponr, Ac., driven along the surface by 
the explosion which accompanies the dismptive discharge 
at the point. This electrification would favour the ^H«ad 
of a positive, but hinder that of a n^ative diachaige. 
There is, in all probability, a connectian between this 
phenomenon and the peculiarities of positive and negative 
brush and other discharge in urj Riess, indeed, snggcsts 
an explanation of the latter somewhat similar to the above. 

There is another class of figures, to which Biess dvea the n^ 
of electric imwes, of which the foUowing may b« takea ** ■ Qrp«L 
A lignet or other engraved piece of metal ia placed on a pUa of 
insn&ting material, and tt^Uy electrified by means of a drriole 
or otherwise positively or n^atively for half an hour or so. when 
the me(al is removed and tbe plate dnsted, in exact fisors of the 
stamp appears, consisting of a red or yellow background on which 
the engraved lines stand out frea from dust. There iano diSerence 
between positiTe and negative electricity here as far as /am is con- 
cerned, and tbe colonr of tbe figure indicates charge on the plate 
opposite to that on the metal. The phenomenon appean to be 
due simply to the electrific«ti(ni of parts of the iion..condiicting 
surface oppoeite the metaL 

Another class of phenomena, to which Biew give* tlta name n(ai 
■econdsry, depend, not on tbe electrification of the sntfaee, bnt on of Ki 
pennaneat alterations produced by tbe discbarge, whether in tha sto. 
tonu of spark or otherwise. Sometimes these are dit«ct1y visible 
to the eye or touch, e.g., the rougheoing and discoloration which 
mark the path of the spark over a polished glass surface. In sane 
casee tbey aie chemical alterations, which may be shown by means 
of the proper reagents, c-ii. , the separatloQ of the potash in the 
spark traces on ^ass. In certain casrs they become evident on 
breathing apon the glaas; of this description are theimuesof Kars- 
ten. Apiece of mirror glsss is placed on an uninsnlated metal 
plate, and on the glass is placed a coin or medal. Sparks an takeo 
for some time between the coin and an electric madiine, and'then 
the glass plate is recooved and breathed upon. A representation of 



1 and Bleetrodynamia,* 
Mention has already been made of the discovery of Oa- 
Bted, that the electric current exerts a definite action on a 
magnetic needle placed in its neighbourhood. This dis- 



' First used by VUlarsy in 1788. 

■ Throughoat this section the reader Is supposed to be familiar with 
the eiperimental laws of nagnetism (see art HAonEim}. If be 
desires fally to andentuid the mathemstlcal developmanta that ocnr 
ben and there, an occsstoDal reference to the analysis osed In tbe 
theory of magnetism will also be Daoeesary, if he i* not ainady faoiUar 
with it 



..1 



ELECTEICITY 



67 



tomy formed the Btartiiig-pomt of that division of electrical 
adence with which we are now to deal. It was natural, once 
the action of a correut' on a magnet was observed, to look 
(or the reaction of the magnet on the current, and after 
•eeing two currents act on the Bame magnet, it was reason- 
able to expect that the currents would act on each other. 
Tet it may be doubted whether the first of these results is a 
le^timate deduction from the discovery of Oersted, and the 
ateoad certainly is not so. Before we can apply the prin- 
cqde of the equality of action and reaction we must be quite 
certain of the eoorce of the vkoU of any action to which the 
I«inciple is to be applied. Again, two bodies A and C 
may act on B owing to properties acquired by virtue of B'a 
jseeence, so that in the absence of B they need not neoes- 
Miily act on each other. A good example is the case of two 
jMeces of perfectly soft iron, each of which will act on and 
be acted on by a magnet, bnt which will not act on each 
Other when the magnet is not near them, 

^le questions thus raised by Oersted's discovery were 
*n-«zperimentally settled by Ampere. He found that a magnet 
yy or the earth (which behaves as if it were a magnet) acts on 
the current, and the direction of these actions is found to be 
omsirtent with the principle of equality of action and reac- 
tion. As no experiment^ fact h^ yet been quoted against 
the application of this principle in such cases, we shall 
assome it henceforth. Ampere also discovered the action 
of one electric current on another, and thereby settled the 
second question. We may conclude, therefore, that the 
space aorrounding an electric current is a field of magnetic 
force just as much as the space around a magnetized body. 
The next step is to determine the distribution of magnetic 
force, or what amounts to the same thing, to find a distri- 
bntum of magnetism which shall be equivalent in its meg- 
■etie action to the electric currenL This also was cora- 
[rfetely accomplished by Ampire. In expounding his 
reenhs we shall follow the order of ideas ^ven by Maxwell,* 
which we think aETorda the simplest view of the matter, and 
is the beet practice guide that we know of through the 
somewhat complicated relations to which the subject intro- 
daces na. We shall in addition give a sketch of the actual 
oaarse which was followed by Ampere, and which is adhered 
to by the Continental writers of the present day. 
da. It results alike from the fundamental experiment of 
td Ampire and the elaborate researches of Weber, to both of 
which we shall afterwards allude, that an electric current 
dreulating in a small plane closed circuit, acts and is acted 
vpon magnetically exactly like a small magnet placed per- 
pendicolar to its plane at some point within it,' provided 
the moment of the magnet be equal to the strength of the 
eorrent multiplied by the area of the circuit,* and its north 
p<^ be so {daced that the direction of the axis of the magnet 
(tnta S-pole to N-pole), and the direction in which the 
enirent circulates are those of the translation and rotation 
(rf a right-handed (ordinary) screw which is being screwed 
in the direction of the axis. In this statement we have 
BpcAen of a ftnall closed circuit. The word " small " means 
that the largest dimensions of the circuit must be infinitely 
smaller than its distance from the nearest magnet or electric 
current on which it acts, or by which it is acted on. 

We may break up our small magnet into a number of 
nmilar magnets, and distribute them over the area of the 
small circuit, so that the sum of the moments of all the mag- 
nets on any portion v of the area is'irt, where i is constant, 
Tf e thus replace the circuit by a " magnetic shell ' of strength 



* " Oomat " ii mad hara tud In eomcpondlng cum u tu abbre- 
tUoa for tlw " Um Unur oondactor ooarsying ■ camnt." 

* ,n»friii» <md Magnttitm, toL 1L §§ 47G, tui. 

* Natonllr tlw cratn of tha ana it It ii irnimctrieal. 

* Wa ^11 aaa dlracUy what iritem at nnlti thia 



t, which, if we choose, may be represented by two layers 
parallel to the area, one of north the other of south mag- 
netism, the surface density of which is i -i- d, where d is the 
distance between the layers.^ 

Starting from the principle thus laid down we can derive Flslta 
all the laws of the mutual action of magnets and electric '=i'calt 
currents. """ 




Consider any finite circuit ABC (fig. 29). Imagine it Sie£^ 
filled with a surface of any form, and a network of lines 
drawn on the surface 
aa in the figure, di- 
viding it up into por- 
tions, such as abed, so 
small that they may be 
regarded as plane. It 
is obvious that any 
current of strength i 
circulating in ABC 
may be replaced by 
a series of closed cur- 
rents, each of strength t circulating in the meehes (such as 
abed) of the network on the surface ; for in each line such 
as 6i: we have two equal and opposite currents circulating 
whose action must be nil. Now, we may replace each of the 
small circuits by a magnet as above, or by a magnetic shell 
of strength t. The asaemblage will constitute a magnetic 
shellof strength t fillingup the circuit, whose magnetic action, 
at every point eatermal'ta'iha shell will be the same as that 
of the current. The north side of the shell is derived from 
the direction of the current by the right-handed screw 
relation given above. 

If (fS be an element of tne surface of a magnetic shell of 
strength a, D its distance from P, and 6 the angle which 
the positive direction of magnetiiation (which is normal to 
cfS) makes with D. then £e magnetic potential' at P ia 
given by 

'" .... «). 

the integration extending all over S. 

When properly interpreted this double integral ia found 
to represent the " solid angle " subtended at P by tlte surface 
S, or, as it may also be put, by the circuit ABC which 
bounds iL Hence, solid angles subtended by the north 
side being taken as positive, and the usual conventions as 
to sign adhered to, we may write 



''//-V- 



(2). 



where oi is the solid angle in question. 

We see, therefore, that the potential of a magnetic shell Potan- 
at any point P is equal to the product of the strength of ^' 
the shell into the solid angle subtended by its boundary at 
P. Now the potential o? such a shell is continuous and 
single-valued at all points without iL (With points within 
it we are not now concerned, since the action of tie current 
at such points is not the same as that of the shell) If, 
therefore, a unit north pole start from any point P and 
return to the same, after describing any path which does 
not cut through the shell, i.e., does not embrace the cturen^ 
the work done by it will be nil. Let us now examine what 
happens if the path cuts through the shell S. Take two 
poinU P and Q, infinitely near each other, but the one P 
on the positive side, the other Q on the negative side of the 



• This limiUUon l> the eqniralent of th« limiUtion imoa applied to 
the slBmanUry plana circait, and follows theretrom. , , „ . 

' We De»l acaiwly remind the reader that aU the deflnltloiie of 
potential, &e., in lbs theorj of alectroaUtlta apply here If wa aoMl- 
tuta + and - magnetiiiD tor -I- and - electrleitj, Tlie nuit of -f 
tDagoatism li •ometimea calleil ■ onit north pole. 



68 



ELECTRICITY 



[bleotboicaonbtibic, 



shelL In passing from P to Q, without cutting the shell, 
the solid angle (u decreases by 4ir infinitely nearly. Now, 
during the passage from Q to P we may not represent the 
action of the current by S, but nothing hinders us from 
representing its action by another shell S', which does not 
pass between Q and P, but is at a finite distance from either 
of them ; for it will be remembered that the shell which 
represents the action of a current i is definite to this extent 
merely — that its strength is t, its boundary is the circuit, 
and it does not pass through the point at which the action 
is being considered. But infinitely little work, owing to the 
action of S', is done in passing from Q to P. Hence the 
work done by a unit pole in going once completely round 
any path which embraces the t;urrent once is iiri. 

To reconcile this result with the continuity of the mag- 
netic potential of a linear circuit, for the existence of which 
we have now furnished sufficient evidence, we must admit 
that the potential of a linear circuit at any point P is 
V = i(u} + 4wir), where n is any integer. In other words, V 
is a many- valued function differing from t times the solid 
angle subtended at P by a multiple of iiri. If we pass 
along any path from P and return thereto, the difference of 
the values of V, or the whole work done on the journey, is 
zero if the path does not embrace the circuit, irnri if it 
embraces^ it n times 
Linear '^^^ considerations enable us to determine the action of 
circuit in any closed current on a magnetic pole, and consequently on 
magnetic any magnetic system. We have next to find the action on 
a linear circuit when plaeod in any given magnetic field, 
whether due to magnets or electric currents. This we do 
by replacing the circuit acted on by its equivalent magnetic 
shell. 

If the potential at any point of the magnetic field be V, then the 

S otential enersy of a magnetic shell S, of strength t, placed in the 
eld is given by 

M=#OS-f -S)'«; • • (3). 

where {If m, n) are the direction cosines of the positive direction 

(soath to north) of the normid to the element dS. Since, so long 

as the magnetic force considered is not due to S itself, there is none 

of the magnetism to which V is due on S, we may ¥rrite - a, - 6, 

dV dV dV 
- c for ^ » ^ * rf~ * ^here a, b, c are the components of the 

magnetic induction. • Then, if N — j(7" ( to + ttiJ + nc)dS (i. « . , — the 
surface integral of magnetic induction, or the number of lines of 
magnetic force which pass through the circuit), we may write 

M--iN (4). 

From this expression for the potential energy of the 
equivalent magnetic shell we can derive at once the force 
tending to produce any displacement of the circuit regarded 
as rigid. 

Thus let ^ be one of the variables which determine the position 
of the system, then the force * tending to produce a displacement 
d^ ii given by ^^ + c2M — 0, or 



field. 



dp 



(5). 



Hence the work done during any displacement of a 
closed circuit, in which the current strength is i\ is equal 
to i times the increase pioduced by the displacement in 
the nimiber of lines of force passing through the circuit. 
The force tends, therefore, to produce the displacement or 
to resist it, according as the displacement tends to increase 
or to diminish the number of lines of force passing through 
the circuit It is evident, therefore, that a position of 
stable equilibrium will be that in which the number of 
lines of magnetic force passing through the circuit is a 

* On the space relations involved here see Maxwell, vol. i. § 17, &c. 

* Magnetic induction is used here in Maxwell's sense. It coincides 
in meaning with '* magnetic force" at points where there is no mag- 
netism. " Line of force " in Faraday's extended sense is synonymous 
with " line of induction" in Marwell's sense. 




maximunL If that number is a miniTminrij we have a case 
of unstable equilibrium. 

Maxwell^ has shown how we may deduce from theActki 
above theory the force exerted on any portion of the circuit <* ^ 
which is flexible or otherwise capable of motion. " If a ^^^ 
portion of the circuit be flexible so that it may be displaced '^ 
independently of the rest, we may make the edge of the 
shell capable of the same kind of displacement by cutting 
up the surface of the shell into a sufficient number of 
portions connected by flexible joints. Hence we conclude 
that, if by displacement of any portion of the circuit in a 
given direction the number of b'nes of induction which 
pass through the circuit can be increased, this displace- 
ment will be aided by the electromagnetic force acting on 
the circuit.** 

From these considerations we may find the electromagnetio 
force acting on any element ds of the circuit Let PQ (fig. 80) be 
the element ds belong- 
ing to the arc AB of any 
circuit. Let PJ$ be the 
direction of the magnetic 
induction * at P, and JB 
its magnitude. It is 
obvious that no motion 
of PQ in the plane of 
PQ and P% will increase 
or diminish the number 
of lines of force passing 
through the circuit ; con- 
sequently no work will 
be done in any such dis- 
placement. Hence the 
resultant electromagnetic 
force R must be perpen* 

dicular to the plane _, .. 

QP». Let PR be a Fig. 80. 

small displacement perpendicular to this plane, the work done in 
the displacement is R.t*R, and the number of lines of force cut 
through is i times the rectangular area PQR multiplied W the com- 
ponent S sin of the magnetic induction perpendicular to it. Hence 
we have 

RxPR-u29xPRxSsina, 

i.e, R— i(29|$sin9 (6). 

Hence the resultant electromagnetic force on the ele- 
ment ds may be determined as follows : — Take P|p in the 
direction of the resultant magnetic induction (magnetic 
force) and proportional to i^y and take PQ in the direction 
of ds and proportional to it ; the electromagnetic force ^ on 
the element of the circuit is proportional to the area of the 
parallelogram whose adjacent sides are P|p and PQ, and is 
perpendicular to it. The force in any direction making 
an angle <^ with the direction of the resultant is of course 
Rcos<^. The following consideration is convenient for 
determining which way the resultant force acts. It is 
obvious that the force on the element will be the same 
to whatever circuit we suppose it to belong, so long as the 
direction and strength of the current in it is the same. 
Take, then, a small circuit PQK perpendicular to the lines 
of magnetic induction (magnetic force) near PQ, in such 
a way that the direction of the current in PQK (as deter- 
mined by the direction in PQ) is related to the direction 
of the magnetic induction in the same way as rotation and 
translation in right-handed screw motion ; then the ele- 
ment PQ tends to move so that the number of lines o^ force 
passing through PQK increases.^ 

• BUctricity and Magnttiam^ vol. ii. § 490. 

^ " Resultant magnetic force," if there is none of the magnetism ffVh 
ducing it at P. 

^ We need scarcely remind the reader that this is a pondennnotiTe 
force acting on the matter of the element of the circuit. There is do 
question of force acting on the current or the electricity in it. 

^ From this may be derived the following, which is often veiy con* 
venient. Stand with feet on PQ and body idong the positive dizecttoii 
of the line of magnetic force and look in the direction of the 
rent, then the force is towards the right hand. 



BI«10TB01IAOinBTI8M.] 



ELECTRICITY 



69 



Seyeral other ways of remembering this direction might 
be given. Although the above may sound arbitrary and 
look clumsy at first, yet we have found it more convenient 
in practice than some others we have tried. 

We may extend what has been said above to the case 
where part of the magnetic force, it may be the whole of 
it, is due to the current in the circuit itself ; for we might 
suppose the magnetic field to be that due to a shell whose 
boundary coincides infinitely nearly with the circuit. If 
the circuit is rigid, there will of course be no motion caused 
by its own action ; but if it be flexible, there may be rela- 
tive motions; in fact each portion will move until the 
number of lines of force that pass through the circuit is 
the greatest possible consistent with the geometrical con- 
ditions. 
tor It is an obvious remark, after what has been said, that 
BB- the potential energy of the magnetic shell which repre- 
' ^^ sents a current depends merely on its boundary, or, in other 
words, that the magnetic induction or the number of lines 
of magnetic force which pass through a circuit depends 
merely on its form. Hence we should expect to find some 
analytical expression for the surface integral of magnetic 
induction depending merely on the space relations of the 
circuit ; in other words, we should expect to find a line 
integral to represent it. And when the field is that of 
another circuit, we should expect to find a double line 
integral for the mutual potential energy of the two repre- 
sentative shells.^ We shall describe briefly how these ex- 
pectations are realized. 

In the first place, a vector may be found which has the property 
that its line integral taken round any circuit is equal to the surface 
integral of magnetic induction taken over any surface bounded by 
the circuit.' This vector has been called by Maxwell the ** vector 

Sotential*' (It). Let its components be F, G, H. Then applying the 
eflnition to small areas dyaZf dzdx^ dxdy, at the point xyz perpen- 
dicular to the three axes,* a, b, e being components of magnetic 
Induction as before, we get 

dH dO . rfF rfH dO _dF ,^. 

'"dy" dz* ^"dz 'dbi' ^"dx di ' • ^'^• 

These equations might be used to determine F, G, H, and would 
lead to a much more general solution than is here required. The 
fbllowinff synthetical solution is simpler. 

Consider a magnetized particle «n at (fig. 81). Let the positive 
direction of its axis be OK, and 
let its moment be m. The 
resultant force due to m at any 
point P is in a plane passing 
through OK ; hence the vector ^* 
potential 8 at P must be per- 
pendicular to this plane. Let 
Its direction be taken so as to 
indicate a rotation round OK, 
which with translation alons 
OK would give right-handed 
screw motion. Describe a 
sphere with O as centre and 
0? (-D) as radius. Let PQ 
be a small circle of this sphere 
whose pole is K. Consider the 
line integral round PQ, and 
the surface integral over the 
spherical segment PKQ. Since 8 is the same at all points of 
PQ by symmetry, the former is 2vD8in0S, and the latter is 



its direction being that already indicated. 

Suppose now the particle sn placed at Q(xyz) so that the direc- 
tion cosines of *n a re A, /it, r. Let the coordin ates of P be (, ij, (; also 

let QP-D- + V((-a;)'' + (i|-y)»+(C-2)*. Then the direction 
cosines of QPareD^g, D«|, D«^, where p - ^; and we get 
for the component of the vector potential at P 

and two similar expressions for G and H. 

The vector potential of a magnetized body may be got by com- 
pounding the vector potentials of the different elements ; hence, Ix, sion for 
I/A, Ir being the components of magnetization at any point of the vector 
body, we get poten- 

and two similar expressions for G and H. The first part of our 
problem is thus solved. 

Let us, in the second place, apply the above result (10) to the case 
of the two shells which are equivalent to two currents. In a 

lamellar distribution of magnetism . —-M^* ^'i hence the 

dz dy 

volume integral in (10) reduces to a surface integral, and 




Fig. 81. 



* It is important to remark here that we say " of the two represen- 
tative shells," not "of the two circuits," or "of the two currents" 
(see below, p. 76). 

* The mathematical idea concerned here seems to have been origin- 
ally started by Prof. Stokes; it is deeply involved in the improve- 
ments effected in the theories of hydrodynamics, elasticity, electricity, 
*t , by Stokes, Thomson, Hehnholtz, and Maxwell. 

* It is to be noted that the rectangular axes here used are drawn 
thus : — ocB horizonal, os vertical (in plane of paper say), and oy from 

Ik* reader; thus»- \J^ ^ In this way rotation from y to « and trans- 

Utkm along ox give right-handed screw motion, and so on in cyclical 
onlw. 



2irmsin*tf 
D 



Equating these we get for vector potential of m at P 

(8), 



tt-^,ain^ 



F-y/^ll(,,n-Km)(iS 



(11). 



where Z, m, n are the direction cosines of the outward normal to d8 , 
Now the magnetic shell of thickness t and strength t is a lamel- 
larly magnetized body of constant intensity — i-rr. It may be 
looked upon as bounded by two parallel surfaces normal every- 
where to the lines of magnetization, and by an edge generated by 
lines of magnetization. At every point on either of the parallel 
surfaces we have therefore Z— A, m— fi, n^'w; and at the edge 

I — r-T^ ' ^ X> '^^ similarly for m and n. Hence every element of 

the double integral in (11) belonging to either of the parallel surfaces 
vanishes, and tnere remain only the parts on the edge which give 



dx , dy 
since \— — r M 






• f-j ,,..— w. (12) gives the vector potential 
ds da ds 

at ((t}C) due to a magnetic shell S. Let ((lyO b« uiv point on the 
boundary of another shell S, of strength i, and let dv be the element 
of arc of the boundary, then 



-'A't 



+ 045-+H 

da 



^y 



(18) 



is the magnetic induction through S' due to S with the sign 
changed, in other words, the mutual potential energy M. Putting 
for F,G,H their values by (12), we have 



^.ii'fp^^dadc 



(H). 



Double 
line in- 
tegral 
forM. 



where c is the angle between d$ and dv. 

The result of (14) realizes the second of our expectations. The 
double integral arrived at is of great importance, not only in the 
theory of electrodvnamics, but abo as we shall see in the Uieory of 
the induction of electric currents. 

Hitherto we have spoken only of closed circuits, and con- 
sidered merely the action of a circuit regarded as a whole. 
When we did speak of the force on an element of a circuit, j^. 
we deduced this force directly from the state of the mag- p^'slaw 
netic field in its immediate neighbourhood. There is an deduce J. 
order of ideas, however, in which the mutual action of two 
circuits is considered to be the sum of aU the mutual 
actions of every element in one circuit on every element in 
the other. Now, we can easily show, by means of (14), 
that a system of elementary forces of this kind can be found 
which will lead to the same result for closed circuits as the 
theory given above. 

Let the circuit S' be supposed rigid and fixed, and let the circuit 
S be movable in any way with respect to S'; it may even be flexible. 



70 



ELECTRICITY 



L 



Denote the angles between the positive directions of da and ds and 
the direction <S D from d<r to ds by 6' and $, then we have 

^ dD ^ dJ) 
cosa-— .cose'--^, 



« ^ ^ _D ^^ 
ds da dsda 



(15). 



(16). 



Bj means of these we get 

!// D d<f IT * 

The part which is a complete differential has been left ont, because 
it disappears when the integration is carried round closed circuits, 
as we always suppose it to be. Consider now the work done in a 

small displacement which alters D and S, -— , — — , and ds, but 

^ da ds 

not da\ we have 



da ds 



.ii^rn__dDfd^^dD_dZs^^^ 
JJ Dd<rV d* ^ dsf 

J J D da 



dD dZs_ 
ds ds 



dads 



The parts containing Is disappear in this expression, and if 
the rest be arranged by integration by parts as usual, we get 

lU-JJUZiydsda^O ... . . •. (17), 
where R,^y2cos€-8 cosOcose^^ 

Hence the electrodynamical action of the two circuits is 
completely accounted for by supposing every element do- 
to attract every element ds with a force 

— gi~( 2 cos e - 3 cos cos d' j • • (^8). 

"We may therefore use this elementary formula whenever it 
suits our convenience to do so. 

It is very easy to obtain a similar elementary formula, 
which is very often useful, for the action of an element of 
magnetic ^ circuit on a unit north pole. 

We have seen above how to find the action on an element PQ 
{ds) of a circuit in a ^ven magnetic field. Let the field be that due 
to a unit north pole J^ (fig. 32). Then the magnetic induction at 

P is in the direction NPE, and is equal to —-, , if NP— D. Hence 
by (6) the force R on PQ* is perpendicular to NP and PQ, is in the 
direction PM shown in the figure, and is equal to j^^^r. Now, by 

the principle of "action and reaction," the force on N is B in the 



Action 
on 




o- 



Comparison of Theory with ExperimenL — ^The best veri- Agi»- 
fication of the theory which has just been laid down con- ^^^ 
sists in its uniform accordance with experience. We pfo- JJJJJ^ 
ceed to give a few instances of its application, adopting 
now one, now another, of the equivalent principles dednoed 

from it. 

We have already remarked that the lines of magnetic ^^x^ 
force in an electric field due to an infinite straight cnirent 
are circles having the current for axis. It is easy to dednce 
from the fact tlmt there is a magnetic potential that Uie 
force must vary inversely as the distance from the current. 

This may also be proved by means of the formula (19) ; in fiact^ 
the resultant force at P is given by 



B=i/^''^-'yi^.--'''^'= 



2j 



(SO). 



i 



d being the distance of P from the corrent. 

Let AB (fig. 33) be a very long straight corrent^ and Pv^ 
poq an element cb of a parsdlel cur- 
rent, having the same direction as AB. 
If we draw the line of force (a circle 
with C as centre) though O, the 



J;^^^ 



tangent OR is the direction of the '*v 
force at O; hence by (6) and (20), 

2i 
the force on jp(?2 ^ 3^} ^^^ ^^^ ^ lA 

the direction OC ; poq is therefore ^ 

attracted. If the current in poq be reversed, the force 
will have the same numerical value, but will act in the 
direction CO. Hence two parallel straight condnctors 
attract or repel each other according as the corrents in 
them have the same or opposite directions. 



Fig. 82. 

direction PM' opposite to PM, i.e. is equal to a force R acting at 
N in a direction S^M^parallel to PM', togeUier with a couple whose 
moment is R x PN, and whose axis is perpendicular to NP and in 
the plane NPQ. Now a simple calculation, which we leave to the 
reader, will show that for any closed circuit the resultant of all the 
conples thus introduced is nil; hence, since we deid with dosed 
drcoits only, we may neglect the couple. 

The force exerted by a closed circuit on a unit north 
pole may therefore be found by supposing each element ds 
to act on the pole with a force equal to 

Ufa sine (19), 

ffhoee direction is perpendicular to the plane containing 
the pole and the element, and such that it tends to cause 
rotation round the element related to the direction of the 
current in it by the right-handed screw relation. 

^ PQ ii supposed to be dnwn^vM the leader. 




Fi9.U. 



Let AB (fig. 34) be an infinitely long (or very l<Hig) Indiiwd 
^— ► cuifntu 

current, .CD a portion of a current inclined to it^ and 

passing very near it at O. If the 
plane of the paper contain AB and 
CD, then at every point in OD the 
magnetic force is perpendicular to 
the plane of the paper and towards 
the reader, at every point in OC 
perpendicular to the plane of the 
paper and from the reader; hence 
at the elements P and Q the forces acting will be in the 
direction of the arrows in the figure, and CD will tend to 
place itself parallel to AB. If both the currents be re- 
versed, the action will be unaltered; but if the current in 
CD alone be reversed, it will move so that the acnte angle 
DOB increases. 
Hence it is often 
said that cur- 
rents that meet 
at an angle at- 
tract each other, 
when both flow 
to or both flow 
from the angle, 
but repel when 
one flows to and 
the other flows 
from the angle. 

These actions 
may be demon- 
strated in a great 

variety of ways, ^ 

Figure 85 shows an anmngement for demonstrating the attnenon 
or repulsion of parallel currents, whiish is essentially that fh»t oMd 
by Ampere. A is an upright consisting of a tube in |pod mtal- 
he connection with one of tiie binding screws I, and with a htUa 
cup JJ, containing a djrop of mercury. A stout wire pMm up we 
centre of the tube, and is insulated from it, but in metallic oooimo- 




Fig.85. 



KLI0TK01U.OKBTiaM.] 



ELECTKICITY 



71 




tion with the (crtw « «ud the cuji q. B is * light condnctor,' con- 
nAing of two puaUelognmi of wire, in which Oie corrent circnlata 
in oppotit* direcCiCFiu. the object of n-hich ii to eliminate tht 
mgnetio sctioD of the earth. The oondoctoi ii hong in the cnpe 

f and c, M> M to be euitf , 

monble iboat a verticu ^\ 

axil. C ia a frame on H I 

which eeTcral tnmi of 

wire are wound, ao that 

when a cuirent ii paved 

UutMUch, we have a nnm- 

b«r oT paratlel eondnc- 

tots, all of which act in 

tli« Mine way on the 

nrtical bnnch uc of tha 

morable condnctor. Ow- 

iag to the opposite direc- 

tioni of tha cnrrenta in 

the tab* and the wire 

iniide it, there ii no 

action on u» due to that 

lart of the Bpparatm. 

It it clear, therefore, that 

the action of C On ut> will pieTail and determine the motion. 

The action of itroigbt condnctort, making an angle with each 
other, mav be shown by means of the conductor D. represented ic 
fig. M, whiiji may be fitted to tbe stand shown in fig. Sfi. 

'**|^ In a very large class of practical coses, circular circuits 
"""• play an important part The lOMt convenieut way of 
deaJiog vltb these, aa a mle, is to replace them by the 
eqaivdent magnets or magnetic shells. The action of a. 
circular circuit may be repreeunted by two layers of north 
and sontli magnetism, whose surfsce densities are ± t-=-T, 
where t is the strength of the current snd r the distance 
between the layers. For details concerning the calcula- 
tions in a variety of cases, we refer the reader to Maxwell's 
JEUetrieii!/ and Mayiietum, vol. iL cap. xiv. 

We may calculate the force exerted (sea Sg. 37) by a circolai 
cnnent AB on a unit north pole at its centre C, as .- . 
foUowi. Replace the wurent by two discs AB and 
A'B', of north and south nugnetism, the distance be- 
tween which is T ; the surface densities are -t-*-i-T and 
-^■^•T. Ths fint of these exerts a tepulsire force 
S>i4>r, the second an attractive force 
Sw<+T(l-co»iA'C3Tj 
bsnoe tha itsultant repulsiTe force is I 

a«ca»lA'(rB' +T- 2iH 4t , 
r being tha radios of the disc. Hence a unit of length 
U the currant exerta a force t4-r> at the distance r. "g- 87. 

it of It followfa therefore that the statement of our funda- 
"^ mental principle (p. 67) involves a unit ot current strength 
'"'^ such that nnit length of the unit current, formed into an 
arc whose radius is the unit of length, exerta a unit of 
force on a unit pole placed at the centre of the arc. From 
this statement and the definition of a unit negative pole it 
follows at once that the dimension of the unit of current 
is [LIMIT-'], 
moid. One BTiangement of circular currents has become 
famous from the part it plays in Ampere's theory of 
magnetism. A wire wound into a cylindrical helix, such 
as that represented in figure 33, the ends of the wire being 
returned paral- 
lel to the axis 
of ths helix, and 
bent into pivots, 
so that it can be 
hnng upon Am- 
pere's stand (fig. 
35), is called a *"* 33- 

BolDnoid. Tbe conductor thus formed is obviously eqni- 
Talent to a series of circnlar currents disposed in a nni- 
Corm manner perpendicular to a common axis. In the 
caae repitaent»l in figure 38, this axis is straight ; but 
tha name solenoid is not restricted to this particular case, 



i 




and what we are about to advance will apply to a solenoid 
whose axis is a curve of any foroL 

Let there be nd* of the circular currents (each of area 
A.) in the arc (if of the axis of the solenoid. As we sup- 
pose the distribution to be uniform, n is constant We 
may suppose each current to be placed at the middle of a 
length - of the axis, which it occupies for itself. Hence, 
if each circular curreut be replaced by a shell of thickness 
- , the surface densities of the magnetism on each of these 
shells will be * nt, and the north magnetism of each shell 
will coincide with the south magnetism of the next; so 
that the whole action at pointt external to the toUnoid 
redacBS to the action of a quantity niX of magnetism 
spread over one end of the solenoid, and a quantity - nik 
spread over the other. Tbe positive or north end of the 
solenoid is obtained, as usual, from the direction of the 
current, by means of the right-handed screw relation. If 
A be very small, or if the ByBt«m acting on, or acted upon 
by, the solenoid is at a distance very great compared with 
the dimensions of A, then we may suppose the representa- 
tive msgnetism concentrated at tha ends of the axis of the 
solenoid. 

Hence tho particular arrangement of electric currents, 
which we have called a solenoid, acts and is acted on 
exactly like an ideal linear magnet (whose poles coincide 
with Ute ends of its axis). 

Thus the north pole of a magnet or solenoid repels the 
north end and attracts the south end of a solenoid; a 
solenoid tends to set under the action of the earth, its 
north end behaving like a magnetic north pole, and 
so on. 

In a cylindrical bobbin wound to a unifonn depth with silk' Oylin- 
covered wire we hare an arrangement which is eqiiivilent to adrical 
number of solenoids all having a common axis. Ejieh of theee bobUa. 
solenoids maybe replaced by the equiTslent terminal disci of posi- 
tive and negative nugnetism, and the external action of tbe wUols 
thus calculsted. The magnetic diK at each end will, of course, 
not be of onifonn density,* but if the points acted on be at a 
distance which ia infinitely great compared with the lateral dimen- 
■ions of the bobbin, ws may collect the msgnettsm at the ends of 
the ui« ; the quiuitities will be 

where a and i are the outer and inner radii of tha shell of wirs, m 
the number of layers in the depth, and n tbe number of turns per 
unit of length of each layer. The magnetic moment of the bobbin 
is theiclare 



Bip(^ (*' + aJ-hJ'), 



The above is a simple case of tbe kind of calculation Websr's 
on which Weber founded his verification of Ampere's expsri- 
theory. He did not, however, replace tbe circular currents 2l*°J*' 
by the equivalent magnetic distributions, but calculated j_^ 
directly from Ampire'a formula (18). m 

The instrument (electrodynamometer) which he used in 
his experiments was invented by himself. It consista 
essentially of a fixed coil and a movable coil, usually bus- 
pended in the bifilar manner, and furnished with a mirror, 
BO that its motions about a vertical axis can be read off 
in tbe tuhjtctive manner (see art Oaltanohetkb) by 
means of a scale and telescope. Two varieties of the 
instrument were used by Weber. In one of these (A), ths 
movable coil was suspended within the fixed coil ; in tha 
other (B), the movable coil was ring-ehaped, and embraced 
the fixed coil, which, however, was so supported that it 
sould be arranged either inside the movable coil or outside 
it at any distance and in any relative position with respect 
■ Tbt rswler will sasUy And ths Uw for himssUL 



ELECTRICITY 



[klbcttbomacktobil 



to it We do not propose to go iato detail respecttag 
Weber's eiperimenta, but merely to iodicate their geneml 
cliaracter and give some of the results. Those desiring 
further information will find it iu §§ 1-9 of the Eieetro- 
dynamitcke MaaAegtimmunffen. 

Webw first showed that the elictrodynamio »otion between two 
parts of a piece of apparatus truTeraed by the same current varies as 
theaquara of tlie cnrrent. Apparatus A waaarranged with the plane 
of ita filed coil in the magnetic meridian. The movable coil was 
concentric with the fixed one, but its plane was perpendicular to the 
magnetio meridian. The current of 1, 2, or S Grove's cells was 
sent through the fixed coil and through the suspended coil ; but as 
the deflection with this arrangement was too great, the latter was 
shunted bj connecting its terminals by a wire of small but known 
resistance. A meaauremeDt of the firil funner of the Btrensth of 
the current was fonnd by observing the deflection prodncod by the 
cnrrent in tie fixed coil on a mngnet suspended in ita plane at a 
coDTenient distance north of it. Alter the necessary correctious were 
applied, the following results Were obtained : — 



. 


U H' 


Dili. 


3 uo-on 

2 198-266 
1 1 60-916 


108 -WB 
72-398 
S6'S32 


]08-]*i 
72-689 
3fi-788 


-0-282 
+ 0-191 
+ 0-*54 



when n is the namber of cells, D the electrodynamio force on 
the anapended coil, expressed in an arbitrary unit, M the force on 
the magnet, M' the force on the magnet calculated frora ^/D by 
means of a constant multiplier. The agreement between M and M' 
la within the limits of experimental error. 

In another series of experiments Weber used the apparatna B 
described above. The suspended coil was arranged with ila axis in 
the maenetio raeridian, and the fixed coil set up with its axis 
perpendicolar to the magnetic meridian. Experiments were made 
with the centres of the two coils coincident, and with tha centres in 
the same horiiolital plane, at distances of 300, 100, GOO, and 600 
millimeCrM, the fixed coil being, in one set of experiments, east or 
west from the suspended coil ; in another set, north oc aouth. In 
the present series of experiments the strength of the cotrent was 
measored by means of a mag^net acted on, not by the fixed coil, but 
by another coil in circnit with it. After proper correctioui, the 
following results were arrived at :-^ 



a 


p 


P- 


Q 


V 





22960 


23680 


2S9«0 


226SO 






189-03 


77-11 










84-77 








89 37 


18-21 






mis 


22-fli 







where d ia the distance between the centres ot the coils, P the 
couple ' exerted on the movable coil when the direction ot that 
diatance is perpendicular to the meridian, Q the couple when it is 
in the meridian. V and Q" are the values of the same eonples cal- 
culated from the theory of Ampere. The agreement here again is 
as near as could be expected. 

Weber further showed that the deflections (v, w) of the Kupeuded 
coil, calculated by means of the formnln 
tanv^ad-' + Bd-* 
tanio=iarf-' + 7rf-« 
In the two cues where the centres of the coils were at a considerable 
distsmce apart, aereed with observation within the limits of axperi- 
meutal error. Now these formula are identical with those estab- 
lished by Gauss for two magneta with their axes placed lite the 
axes of the coils. This agreement therefore is an experimental 
proof that the coils are replaceable by magnets. 

On the whole, therefore, the experiments of Weber' con6nn the 

thsoiT ot Ampire, as far as erariment can test it They form, 

therefore, a sufficient basis for the proposition on which we founded 

OUT theory ; for this proposition leads to the same result for closed 

circuits as the theoiy of Ampire. 

Eiperj- The action of any cnrrent on a magnetic pole, and hence on any 

nwnts of nia([net, may bo calculated either by replacing the circuit by an 

Blot and equivalent shell or bv means of formula (IB). We have already 

StTut. found this action in the particular case ot an infinitely long straight 

current. This result was originally found experimentally by Biot 



a standard cnireni strength by means of the magnet 



' Reduced 
deflections. 

■ ForanotharvetiflcatlonbyCaiin, ieaWledamaan,OaI«,Bd.U. f 41. 



and Savart, and Laplace showed that it followed from their reaolt 
that the force exerted by an element ot the cnrrent Tariea inrerady 
as the square of the distance. The fact that a circular current *ett 
on a magnetic pole at its centre in the aome way as ■ xig-zafr cur- 
rent which is everywhere very nearly coincident with it, leads, 
when properly interpreted, to the concksion that the foreo variea 
aa sin0. In this way formula (16) was originally arrived at, inde- 
pendently of Amplre's theory. 

A great variety of instances might be given of the action ot a Ei 
magnet on a current. The earth, for instance, acts on a orcutar ac 
current, hung up on Ampere's atand: the current, being movable 
about a vertical axis, will turn until the maximom number of tha 
earth's lines ot magnetic force pass through it — i.e., it will set with 
its plane perpendicular to the magnetic meridian, in such a way 
that the cuirent, looked at from the north side, goes raond in th* 
opposite direction to the bands of a watch. 

A very simple wav of showing the action betweeo magnets uid ]> 
currents was devisea by De la Rive. A small plate of copper and a R 
small plate of zinc are connected together by a wire passing thron/^ ll< 
a corV and making a circuit of several turns ; the cork is placed in hi 
a vessel containing dilute sulphuric actd, and floats on the lurfacc, 
carrying the little circuit about with it. Such a circuit will set 
under the earth's action, and may be chased and turned about, Ac, 
by a magnet. After what has been already said, however, ancll 
experiments ofier no new point of interest. 

Mlectramoffnetic Rotation*. — It is obviotu tlut DO O 
invariable system of electric curreats caa produce con- ^' 
tinuous rotation of a magnetized body. For, suppose an ^ 
elementary magnet, whose action may be rupreaented by 
tiro poles of strengths ^ tn, to describe any path and to 
return exactly to its former position ; either it has or has 
not embraced the circnit in its path; if it hsa not, no woil 
has been done on either pole ; if it has embraced the circnit 
n times, an amount of work inmn' has been done on the 
north pole, and an amount — 4nnin-i on the south; on the 
whole, therefore, no work has been done on the magnet 
As any magnetized body may be conceived to be made up 
of such elementary magnets, it ia obvious that it is impos- 
sible for such a body to rotate continnouaLy, doing -<iioA 
against friction,' i&c. 

The same is obviously true if we replace the magnet \fj 
an invariable system of electric carrents. 

If, however, part of the electric circuit is movable with 
respect to the rest, and communicates therewith by means 
of sliding contacts or the like, continuona rotation of part 
of the circuit may occur. Again, if by any artifice the 
magnet can be transferred every revolution from one side 
of the current to the other, continnouH rotation of the 
magnet may result. Lastly, if the direction of the current 
in some part of the apparatus be always reversed at a 
certain stage of the revolution, continuous motion may 
ensue. 

Rotations of the first and second class were first dis- Fi 
covered by Faraday, and the ground principle of most of ^ 
the pieces of apparatus used in demonstrating them is that ^ 
originally used by him. 

One of the simplest cases ia the rotation under the action of the 
vertical component of the earth's magnetic force. Let ABC (fig. 
39) be a horizontal cireular condnc- - 

tor, OP a conductor pivoted at 0, j^ — *-~,.,,^ 

havingslidingcontactaf PwithARO. / X_ 

Let a current ' -- - 
leave it at P, 
O and thence 
The magnetic 



onlactal rwiuiAHU. X _, Xp 

; enter ABC at A, and / -'^V/A 

lowing through PO to / y^ \ 

to the battery again. I J^ ] 

force at any element ' Al O I 

1 vV 



o OP and 



force on the element will h 
in the plane of ABC, in the directioi 
of the arrow pi* and will be equal to d »o 

•Rrfr(R=rerticalcom|>Qnentofearth's "K" '"• 

force). Hence the moment about ot the forces acting on OP la 
/iRrdr, i,e. iOP'Ki, which is independent of the position of OP. 
OP will therefor* rotate about 0, with an aiieular velocity which 
will go on increasing tuitil the work lost by friction, ftc, dniii^ 
each revolution is equal to irOP'Ri. 



■uonujiuoHiTreif.] ELECTRICITY 

Amptn hai given > goural tIiNT7 of thi ToUUon of > drcii 



78 



tliB utioti of > nugnBt Lat AB (fig. 40) ba auf circuit, irhicb we 

may lappOM connecttd 

witii tbe uii of ths msg- 

net, bat fi«e to rotate 

aboat it. Wa nppoae the 

munet repUccd hy qnanti- 

tim ±w -• -5 ' 




Pig. *0. 



it* poles. Tako the axis of 
the niB^et for aiia of i, 
and the othrr axei ai in 
the Bgnre, O being the 
ecDtre of the magnet, ud " 
let 0N = 08 = e. Let PQ 
be aBf anil* of AB, and let 
the coordinate* t^ P be 
z, V, I ; then if I, m, n be the 
diractioD codoeB of NP, 
and NP-D, we have 
Dl = x, Dm-v, Dn-i-ej 
alio the directioQ coainea 
of Pjg, which ie perpen- 
dicnlar to NP and FQ, 
and ia the direction of the 

foroe exerted bf the pole N o: 

Binca bj fonnnla (S) the componenta of the force acting on PQ 

Henc«, if K denote tbe moment of thew forces aboat OZ, we have 
from the north pole alone 

If we cabatitute the valoea of ^ m, n thi« redacei to 

If tbenton 0,. a,, St, a, denoto the angles BNZ, AKZ^ BSZ, 
ASZ, we liaie, adding Ibe reralta from both poles, 

E = Bii(co«0,-coaa,-cos3i + cosa,) , . (21). 

It follows from thia remarkable formula that the couple 
K tending to tarn a part AB of an electric circuit about 
tbe axis of a magnet depends merely on the poajtba of the 
eadi A and B. 

In particnlar, if A coincide with B, i.t. if AB form a 
closed circuit, or if A and B both lie on parts of tbe axis 
not included between N and S,' the couple will be ni7, 
and there will be no rotation. 

The application of this formula to cases where there are 

■liding contacts at A and B not lying on the axis presents 

no difficulty ; we leave il to the reader. 

Matlm Several of these rotations may be exhibited by means of the 

ppu«< appantos represented in figure 41. ABC is a horiioutal toil of wire 




' Wt might conaidar what would happen if A or B la; on K3, bat 
the CM* never ariaea In piactice, for all mi^net* have a finite thickiKsa 
<iat an this antt)«A Wiedeniun, B<1. ii. 1 119). 



terminating at the binding screwi a,t. FO is ■ ring-shaped tnmgh 
of mercnry for the sliding contacts. A wire connect* the mercnry 
with Uie binding tcrew d. DE ia an npright sapport screwed into 
a metal base D in connection with the binding screw e, and ter- 
minating ahoTo in a mercnry cup E. When required, DE can be 
replaced by the shorter inpport* I^E' and D'E". HLK ia a support 
for a screw L, which carnaa an adjustible centra. 

1. Poise in tbe cup E the vire atirmp HN, so that the ends just 
dip in the mercniy trongh. Then, if a strong cnrrent be sent trtaa 
ctod, MX will rotate (in notthem latitudes) in a direction opposite 
to the hands of a watch. 

2. If we fix a vertical magnet n"*" to DE by means of a clip at 
Y, then the rotation will lake place with a weaker current in the 
Bamo direction a* before, if tbe north pole of the magnet be upwards 
(as shown in figure), but in the opposite direction if the magnet 
be reversed. 

S. Beversing the current alona in either of the last two case* 
causes the direction of rotation to be reversed. 

4. The magnet may be renioTnd and a current sent from a to ft 
round ABC in the direction opposite to the hands of a watch. The 
result is the same as for the mngnet with iti north pole upwards. 
if the corrent in ABC is reverted, the rotation is reversed ; and 

E. The sapport WE,' with the two magneta ni, nV may be acrewed 
into D inatewl of DE, the wire P now dipping into the mercunr. 
If the cnrrent be sent from ctod, the vertical cnrrent in D^ will 
act on > and /, and cause tbe magnet to rotate in the direction of 
the hands of a watch. Tliia rotation ia reversed if the onrreut go 
from il to c: 

A. Wa may consider any magnet of finite size aa made npof s 
aeries of magneta like n» and nV arranged about an axia. Hence, 
if we replace D'E' and the magnets D''E* by the single magnet 
supported by means of tbe pivot L", there will still be rotation. 

iVure 43 represents a very elegant piece of appatatus devised by 
Faraday, to show the ro- 
tation at once of a magnet ^ 
and of a movable conductor. 
The rotating pieces are the 
magnet m, which is tied to 
the copper peg at the 
bottom of G by means of 
a piece of string, and 
swims round the vertical 
current bnoyed up by the 
mercnn* in Q, and the wire 
DE, which ia hinged to D 
by a thin flexible wire, and 
swims round the pole of 
the vertical magnet n's'. 

Another spparalu* in- _. .„ 

vented by Barlow, and '«■ *^- 

known by the name of Barlow's wheel, is represented in figure 4S. 
A current is csused to pass from the mercnry troiwb C along ths 
radius of the disc A through the field of magnetic wrce due to the 





Fluid conductors may also be caused to rotate nnderrtnldn 
the action of a magnet We mentioned in our historical lations, 
sketch the experiment by which Davy demonstrated this 
rotation in the case of mercury. A vanety of such experi- 
ments have been since devised. The following is a simple 
one. Fill a small cylindrical copper vessel with dilute 
sulphuric acid and set it upon the north pole of a power- 
ful electromagnet If a thick zinc wire be connected by 
a piece of copper wire to the copper vessel, and then im- 
mersed in the acid so as to be b the axis of the vessel, a 
current is set up in the liquid which flows radially from 
the zinc to the copper across the tinea of force. The 
VnL — lo 



T4 



ELECTRICITY 



[sucTsoiuamtuiL 



D the directioD of the hands of a 



liquid therefore rotates 
watch. 

AcUonof Moffnetie Action on the Fleetru; DUcharge in Ga*ei. — A 
mienst large number of reiy interesting resnlts have been obtained 
*2^^fl^ concerning the behaviour of the electric discharge in a 
GtumT fi*'*^ "^ magnetic force. We can only make a brief allu- 
sion to the matter here. The ke; to the phenomena liee 
in the remark that the electric discharge in vacuum tubes 
may be regarded as an electric current in a very fieiible 
elastic conductor. It is clear that such a conductor would 
be an equilibrium if it lay in a line of magnetic force 
passing through both its fixed ends. Again, if the flexible 
conductor be constrained to remain on a given surface, 
it will not be in equilibrium until it has so arranged itself 
that the resultant electromagnetic force at each point is 
ptrpendicidar to the flurtacc At each point, therefore, 
the magnetic force must be tangential to the surface.^ 

A perfectly flexible but ineitensible conductor, two 
points of which are flzed, will take such a form that 
the electromagnetic force at each point is balanced by the 
teasioo. Le Rouz fastened a thin platinum wire to 
two stout copper terminals, and caused it to glow by 
passing a current through it. When the terminals were 
placed equatorially between the flat poles of an electromag- 
net, the wire bent into the form of a circular arc joining 
the terminals. When the terminals were placed azially, 
it assumed a helical form. (See also Spottiswoode and 
Stokes, Proe. R. &, 1875.) 
Batktioa The behaviour of tlie light emanating from the positive 
of elso- pole may be explained in general as lying between the two 
^^^^ cases which wo have just discussed. One of the most 
remarkable of these phenomena is the 
rotation of the discharge discovered by 
Walker, and much experimented on by 
De la Bive. This may be exhibited by 
means of the apparatus shown in fig. 44, 
consisting essentially of an exhausted 
Teasel, one of the electrodes in which is 
ring-shaped; a bar of soft iron, covered 
with some insulating material, is passed 
through the ring and £ied to the stand. 
When this apparatus is placed on the pole 
of a powerful magnet, the discharge ro- 
tates as a wire hinged to the upper elec- 
trode would do. 

Owing to the distinct character of the negative light, 
the action of the magnet on it is different from that on 
the positive light. Fliicker found that the general 
character of the phenomena may be thus described : — 
The negative light is bounded by magnetic curves that 
issue from the electrode and cut the walls of the tube. 
The two diagrams in fig. 45 will convey an idea of the 







rig. 4i. 




appMianoe of the phenomenon. Although much tempted 
* Ldd bSTilg UU* prapwtf were ciUad by FlUckaT i^polie coma. 



to follow the subject further, we must be content to refer 
the reader to the interesting papers of Plucker* and 
Hittorf.* An excellent summary will be found in yfiade- 
mauD. 

Ampirr't Method. — Before quitting the subject ofAa- 
electromagnetism, it will be useful, for the sake of com- P^' 
parieon, to give a brief sketch of the method of Ampirc^ ^**^ 
or rather of that modification of the original mediod now 
commonly found in Continental books, which was suggested 
by Aranftro himself, in a note to the Thiorie des Phfnt>- 
ntenet Electrodynamiqut). Ampere starts nith the idea that 
the electrodynamic action of two circuits is the sum of the 
actions at a distance between every pair of their elemecta. 
He supposes, as the simplest and most natural assumption, 
that the force between two elements is in the lino joining 
them. Besides this assumption, his theory resta on foor ex- 
periments.* The first of these shows that, when a wire is 
doubled on itself, the electrodynamic action of any current 
in it is nil. The second experiment shows that this is also 
true, even if one of the halves of the wira be bent or 
twisted in any way, so as never to be far removed from 
the other. The third experiment proves that the action 
of any closed circuit on an element of another circnit is 
peqiendicular to the element. In the fourth experiment 
it is shown that the force between two condoctore remains 
t)ie same when all the lines in the system are increased in 
the same ratio, the currents remaining the same. From 
the assumption, together with the first experiment, it fol- 
lows that the force between two elements is proportional 
to the product of the lengths of the elements, multiplied by 
the product of the strengths of the currents and by some 
function of the mutual distance and of the angles which 
determine their relative position. Hence it may be shown, 
from the fourth experiment, that the force between the 
elements must vary inversely as the square of the distance 
between them. The second experiment shows that we 
may replace Eiuy element of a circuit by the projections 
of the element on three rectangular axes. 

From these results it is found that the force betweea 
dt and d<r must be 

Ai^(co8«-icos(!cosO. 

The constant Te is then determined from the result of the 
third experiment ; and it is found that k must be equal 
to \. The formula is thus completely determined, with 
the exception of A, which depends on the unit of cnireot 
which is chosen. The action of a closed circnit on an 
element is then calculated, and a vector found, which 
Ampere calls the " directrix," from which this action can 
be found in exactly the same way as we derived this 
same action from the magnetic induction. The theory is 
then applied to small plane circuits, solenoids, and so on. 

As was remarked in the historical sketch, a variety of 
other elementary laws may be substituted for that of 
Ampere, all of which lead to the same resnlt for closed 
circuits. 

Maxwell has presented Amp^'s theory in a more general 0<nai 
form, in which the assumption about the direction of the u***" 
elementary action is not made. Neglecting couples, he '^^ 
finds for the most general form of the components' of the 
force exerted by da on ds, 

in the direction o( 0, 

in tha direction of cU sod da respectirdy. 



» Pogg. Am*., dU., dv., cv., cvii., ciiii, 1888, fco. 

* Pogg. Ann., oiiitI., 1869. _ 

' Detail* reapKliog thae eiperimanta, snd otliar mitter i w wittri 



OTDUOTIOH.] 



ELECT 11 ICITY 



75 



Id these eipreesious Q is a function to be determined 
only by fnrther esBomptiun. Q — constant gives Amp6re's 
foimala; Q- - 5- givea the formola of Orsssmann, imd 
•o on. We may in fact conetmct an infinite variety of 
different elementary fonnnUe. The reader interested in 
this subject may conanlt Wiedemann, Bd. ii. §§ 26, 27, 
45-54, Ac., and Tait, Proe. R.3.B., 1873. 
of la our account of the magnetic action of electric car 
■n. nnts do mention baa been made of tbe effect of the proxi- 
mity of soft iron. Under tbe magnetic action of the 
electric circuit soft iron is magnetized inductively. The 
distribution of the lines of force is in general greatly 
affected thereby. The general feature of the phenomenon 1 
is a concentration of the lines upon the iron. By the 1 
proper use of this effect electromagnetic forces of great 
power may be developed. It is not easy to give a mathe- 
matically accurate account of the action, owing to our 
ignorance of the exact law of magnetic induction in power- 
fully paramagnetic bodies. The discussion of this subject, 
however, belongs to Maometish (which see). 

Th« Indwiion. of Electric Currmti. 
k brief account has already been given (see Historical 
Sketch, p. 11) of Faraday's discovery' of the induction of 
' electric currents. The results hearrived at may be summed 
up aa foil owe. 

Let there be two lineu cirmits, A6EE (the prinmry] and CDG 
(the eecoaduy), two poctiolu of which, AB utd CD, ore purallt^l, 
uid nur each other. 

I. When B enmnt is itarted in AB, a transient current nonn 
■ through CB in the opposite direction to the current in AB; whea 

the coireDt in AB u rtead;, no current io CD can be detected ; 
when tbe cnirent in AB ia stopped, a transient current Bowa throueh 
CD in the aame direction as the current in AB. These cumata m 
CD an said to be induced, and may be called ioTctae and direct 
cniranta respectiTely, the reference being to the direction of the 
priniuy. Both inverse and direct cntrenta lost for ■ veij ehart 
time, aed tha qnantity of etectridty which panes in each of them 
ii the same. 

II. If the cirenit AB, in which a etcady current ia flowing, "tie ' 
oannd to approach CD, an mTene current is thereby indncnl in 
CD; whea the circuit AB, under similai circumstances, recedes 
from CD, a direct enmnt is induced in CD. We have already 
mentioned tbst when AB is at rest, and the current in it does not 
vary, there is no current in CD. AB has been supposed to approach 
and recede from CD, bnt the same atatement appliea when CD 
qmroaches and recode* from AB. 

III. When a magnet is magnetized or demaADetiied in the 
neighboorhood of a cirenit, or approaches or recedes from the cir- 
cuit, the effect is the same as if an equivalent* cnrrent approached 
or receded from the circuit. For example, imagine a small circninr 
dnoit placed horizontally, and a vertical bar magnet lowered in j 
the axil of the cirenit with its north pole pointing down u[>on the 
cirenit, the magnet may be replaced by a series of coaxial circular | 
cnirenti {lee above, p. 71), and the motion will indnce a current I 
posing nnmd the cirenit tgsinst the hands of a watch. ' 

Faraday showed how the direction of the induced current 
can be predicted when the variation of the magnetic field 
or the motion of the conductor in it is known, and he gave, 
in his own manner, indications how tbe magnitude of the 
onrrent could be inferred. 

Maxwell has thrown the law of Faraday into the follow- 
ing form : — " The total electromotive force acting ronnd a 
drcnit at any instant is measured by the rate of decrease 
of the number of linea of magnetic force which pass 
through it" 

Or, integrating with respect to the time : — " The time 
iukegral of the total electromotive force acting round any 

with Ampin's theorr, may be found In Harwell, vol. il. S fi02, ic, 
snd la altuost any ContineDtal work on experimental physics. 

» Xxp. Ra., ser. L, ii., (ii.), iiviii., uii., 1881-32, 1851. The 
general atatement in the text is given loi ths reader' s coDrenience, 
■Dd is not meant to be hiatorioaL 

* Kqulvalcot In tha smsa at prodndiig th* ■ 



circuit, together with the number of lines of magnetic force 
which pass through the circuit, is a constant quantity." 

For " number of lines of force " may of course be sub- 
stituted the equivalent expressions, " induction through 
the circuit," or " surface integral of magnetic induction,'' 
taken over any surface bounded by the circuit. 

Some care must be taken in determining the pontile 
direction round the circuit. The following ia a correct 
process : — Assume one direction (D, fig. 
46) through the circuit as positive, then 
I the positive direction round (R) is deter- 
, mined by the right-handed screw rela- 
tion ; if the number of lines of force 
reckoned positive in direction D is de- ^8- M. 

creasing, then the electromotive force is in direction R ; if 
that number is increasing, the electromotive force is in 
the opposite direction. 

This will be clearer if we consider the following ^mple example. 
Let ABCD (Gg. 47) be a horizontal rectangular circuit (AB next the 
reader). In a northern lati- 
tude, the vertical component 
Z of the earth's magnetic force 
ia downwards ; if, therefore, 
tliQ positive direction through 
the circuit be taken down- 
warde, the poBitive direction 
round is ADCB, and the 
number of lines of force „ ,, 

through it is Z.AB.IiC. If rig- il. 

BC slide on DC and AB parallel to itself throngh ■ small distance 
BB' in time t, Z.AB.BC incrtaxj by Z.CB.BB' ; hence the elec- 
tromotive force is Z.BC.BB'-v-t, and acts ia the direction ABOD. 
If D be the velocity of BC, we may write for ths electromotive force 
Z. BC.E. That is, the electromotive force at any instant is pinpoi- 
tional to the velocity. 

The law of Faraday leads to a complete determination 
of the induced current in all cases. We may regard it as 
resting on the experiments of Faraday, and of those who 
followed out his results. 

Another view of the matter of great importance was Theoryof 
enunciated independently and about the aame time by Helm- 
Helmholtz' and Sir William Thomson.* 5hom"* 

Let a circuit carryiDg a current 't move in an invariable mtg- ^gj,^ 
netic field, so that the number of lines of magnetic force passing 
through it is increased by dU, then the work*doce by the electro- 
magnetic forces on the circuit is by Ampere's theory iifN ; also, if 
R be the resistance of the circuit, RCdl is the heat generated in 
time dt. Now if £ he the electromotire force of the battery which 
maintains the cuircnt 1, the whole energy supplied ii Sidt ; hanea 
He must bare 




'SijTl 



(28). 



Hence there is an electromotire force ~ 



- in the moving ciranit> 



Now ^ ia the rate of increase of the nnmberoflineaofforcepast 

ing through the circuit 

We have therefore deduced the law stated above from 
Ampere's theory and the principle of the conservation of 
energy ; at least we have done so for the case of induction 
by permanent magnets, and the same reasoning will also 
apply to the case where the altemtion of the magnetic field, 
owing to the induced current in the primary cjrcnit, ia bo 
small that it may be neglected. 

Wo have now the means of stating in a convenient form Electn- 
the electromsgnetic unit of electromotive force. It is the magnetle 
electromotive force of induction in a circuit the number of "j^^. 
lines of magnetic force through which is increasing atmoti,, 
the rate of one per second. force. 

* Ufier die Erluillung der Kraft, I8J7- 

* Rtp. BHt. Ah., 1848, and Phil. Mag., 1851. 

' All tbe quantities are supposed to be measured In electromsgDetle 
absolute nnlta. 

* We may soppoee this work spent in rating a wcd^t, Jm. 



76 



fjLElCTRlCITY [elsotboiiagnxtio iXBuonoa: 



In the case where the field is dae to a current i", we have by 
formnlie (4) and (H) of last division 

N=i'M (24), 



where M now stands for 



/7"C0S€ 

JJ D 



dad,c extended all over the two 



Electio- 

kinetio 

energy, 

Theor; 

Thorn 

son. 



circuits. M, which depends merely on the configuration and relative 

Sosition of the two circuits, is called the coefficient of mutual in- 
nction. 

An application of the principle of the conservation of 
energy of great importance was made by Sir William 
Thomson to the case of two electric circuits of any form, 
^^°'in which Uie currents are kept constant 

Let two such circuits, the currents in which are u", be displaced so 
that the coefficient of mutual induction M increases by dM. Let 
us suppose that the currents i and H are maintained by two constant 
batteries of electromotive forces E and E', aud that the motion 
takes place «? slowly that the currents may be regarded as constant 
throu^out If R and R' be the resistances of the circuits, Hctt 
the mechanical equivalent of the whole heat generated, and }LdX 
the whole expenditure of chemical energy in the batteries in time dX^ 

H - Ri» + R'i^, and K - Ei + EV, 
K-H-iXE-Rt) + »(E-RV). 

Now, applying (23), 



Ri=E- 1'^ , and RY - E' - t"^ ; 
aX cU 



whence 



E-H-2tV 



vdM 



(U 



or, as we may write it, 

(K-H)<ft=2u-'dM ... . (26). 

Now tVdM is the work done by the electromagnetic forces during 
the displacement which we may suppose spent in lifting a weight. 

Hence, when two electric currents are allowed slowly to 
approach each other, being kept constant and doing work 
the while, over and above the work which is spent in 
generating heat in the conductors, an amount of energy is 
drawn from the batteries equivalent to twice the work 
done by the electromagnetic forces. 

There remains therefore an amount of work as yet 
unaccounted for. What becomes of iti The answer is, 
that the energy, or, as Sir W. Thomson calls it, the ** me- 
chanical value," of the current is increased. But how 
increased 1 When a material system (and we may consider 
the two circuits, the batteries, the lifted weight, &c., as 
such) is left to itself, it moves so that its potential energy 
decreases. In this case, therefore, there must have been an 
increase of kinetic energy somewhere. This energy may 
be called the electrokinctic energy of the system ; according 
to Maxwell's theory, this kinetic energy has its seat in the 
medium surrounding the wire. The energy thus stored 
up is accounted for in the increased development of heat, 
Jcc, when the two currents are broken in succession. 
^-^ . Eetuming now to our general law of induction, let us 
two cir- ^^ite down in the most general form the equations which 
colts. determine the course of the currents in two circuits (A, B), 
in which the form and relative positions of the circuits, as 
well as the current strengths, are variable. The number of 
lines of force which pass through a circuit depends partly 
on neighbouring circuits, partly on the circuit itself. Re- 
taining the notation used above, we may, in the case of two 
circuits, write the first part Mi', and the second part hi; 
where L is a double integral of the same form as M, only 
both elements ds and da- now belong to the same circuit. 
We have, therefore, for the whole number of lines of force 
passing through the circuit A, Mt' + Lt. Similarly we 
have for B, Mi + Ni'. We have therefore by our general 
law, 

£-^/Mi'+LO=Rt ) 

d ( ' • ' (26). 

These are the general equations for the induction of two 
dicuits. The electromotive force of induction in A can bo 



divided into two parts : one of these, viz., ju(}if) is due 

to the circuit B, the other r. (Lt) is due to the circuit A 

itself, and is called the electromotive force of self-inductioQ. 
L is called the coefficient of self-induction for A. Similarly 

— (Ni") is the electromotive force, and N the coefficient 

force of self-induction for B. 

If we have only one circuit then M » 0, and the equation 
for the course of the current is 

E-^(Li)-Rt; 

here there is ofdy self-induction. 

F. E. Neumann, to whom belongs the honour of first Tbeoiyfli 
stating with mathematical accuracy the laws of induction, Nea. 
adopted a foundation for his theory very different from the JJI^ 
one chosen above. His method was based on the law of i^ y 
Lenz^, enunciated very soon after the great discovery of 
Faraday, which lays down that, in all cases of induction by 
the motion of msignets or currents, the induced current has 
a direction such that its electromagnetic action on the 
inducing system tends to oppose the motion producing it. 

Besides its historical importance, this law affords a very 
convenient guide in many practical applications of the 
theory of induction. The reader will find no difficulty in 
verifying it on the elementary cases given at the beginning 
of this division. It can be deduced at once from our 
general law. Consider any circuit in which a current t is 
flowing, and let the direction of the current be the positive 
direction round the circuit. Suppose the circuit to move 
so that the number of lines of force passing through it 
increases, this is the way the circnit would tend to move 
under the electromagnetic forces when traversed by a current 
i; but the electromotive force of induction is in the negative 
direction round the circuit by the general law, and would 
therefore produce a current opposite in direction to t. The 
electromagnetic action on this current would be opposite to 
that on i, that is, would tend to hinder the displacement 
It is a curious fact that a law exactly like this had been 
announced shortly before Lenz by Ritchie, only with the 
direction of the action revet'sed in every case. 

The results of Neumann are identical with those given 
above. The double integral M, which is here called the co* 
efficient of mutual induction of two circuits, Neumann calls 
the mutual potential of the two circuits, and what has been 
c.illed above the coefficient of self-induction of a circuit he 
calls the potential of the circuit on itself. Accounts of his 
theory will be found in Wiedemann's OalvanismtUf and in 
most Clontinental works on electricity. 

Experimental Verification of the Laws ofMutuallnduetiam. 
— It will be observed that, in the law of induction for linear 
circuits, no statement is made respecting the material or 
thickness of the circuit in which the electromotive force of 
induction acts, or of the non-conducting medium across 
which induction takes place. 

Faraday showed that the material of the circuit has no effect.' £zp«i' 
He found, for instance, that when two wires of different metals were mcnti b] 
joined and twisted up together, as in fig. 48, so as to he insulated Findty; 
from each other, no in- y _ ._. , * 

duced current could be ^'^^ ^ •^ ^ ^— "S^^— ^^P^»**^^*^^*^'^Q^^ 
obtained by passing the p. ^g 

arrangement between the ^' 

poles of a powerful magnet. The same result was obtained when one 
of the branches of the circuit was an electrolyte. Lenz* connected 
two spirals of wire in circuit with each other, and placed first one 
then the other, on the soft iron keeper of a horse-shoe ma^et; ao 
long as the number of turns on each spiral was the same, theindnced 

> Pogg. Ann., 1884. 

* Exp. Ret., 193, &c., 1832 ; alK> 8148, Ifcc, 1851. 

' Pogg, Ann,, 1835. 



MLEOtROUAQVWnO INDUOTION.] £iLISCTRICITY 



77 



enrrent was the same, no matter what the material or thickness of 
the wire in each spiraL Since in this case the whole resistance of 
the circuit was always the same, the electromotive force of induction 
must have been the same. 

We conclude, therefore, that the electromotive force ^ of 
induction is independent of the material, and also of the 
thicVnftgft of the wire, so long as the latter is so small that 
we may consider the wire as a linear circuit. 

Lenz made quantitative determinations of the induced 
current by means of the above arrangement. 

The soft iron keeper, with a coil of n windings, was rapidly 
detached fh>m the ma^uet, and the first swing a of a galvanometer 
in circuit with the coil was measured. The quantity of electricity 
which passes in the induced current is measured by sin ^a, provided 
the whole duration of the current is small compared with the time 
of oscillation of the galvanometer needle (see art Galvano- 
MITKB). Again, when the keeper is attached to the magnet, very 
nearly all the lines of magnetic induction* pass through the keeper; 
hence the number of lines of induction which pass through the 
coil is very nearly proportional to the number of windings, and 
therefore, if the resistance of the circuit be kept the same, the 
whole amount of electricity which passes will be proportional to m. 
In the actual experiment the wire was woimd and unwound from 
the keeper, so that the whole resistance did remain the same. The 
following is a set of Lenz's results : — ' 



No. of Windings. 


3 


4 


8 


13 


16 


30 


sin 4a 


0-0491 


0-1045 


0-2156 


0-3319 


0-4470 


0-5594 


Sinia-i-fi 


0246 


0-0261 


0270 


0-0276 


0-0279 


0-0280 



The value of sin |a -S- n is very nearly constant It increases a 
little as the number of windiikgs increases, as ought to be the case, 
for, although most of the lines of induction pass through the keeper, 
yet all do not, and a few more are included when the number of 
turns is increased. 

act of Faraday made special investigations in search of the 

diom. effect of the medium across which induction is exerted. 
He found ^ that no effect on the integral current was pro- 
duced by inserting shellac, sulphur, copper, &c between 
the primary and secondary coils. The insertion of iron or 
any strongly magnetic body, of course, produces an effect, 
because the distribution of the lines of magnetic force is 
thereby altered, and therefore, by our general law, the 
electromotive force of induction will be correspondingly 
affected. We conclude, therefore, that the electromotive 
force of induction is independent of the medium across 
which it is exerted.^ 

It must be remarked, however, that in the case of con- 
ducting media, the statement is subject to a certain limita- 
tion, the nature of which follows from the law of induction 
itself. For there will be induced currents in the interven- 
ing medium if it be a conductor, and these currents will 
disturb the lines of force while they continue to flow. 
These currents are transient, however, so that their integral 
effect on the number of lines of force passing through the 
secondary is zero. It is obvious, therefore, that, if we 
replace '' electromotive force" by " time integral of electro- 
tive force extended over the whole time that the induction 
currents last," the statement will still be true. The only 
effect, therefore, of interposed conducting media is on the 
iime which the induced currents take to rise and faU. 

iber's Weber^ applied his electrodynamometer to test the laws 

mi' of induction. 

BtS. 

The suspended coil was caused to oscillate when there was no 
enrrent eitner in it or in the fixed coil, and the logarithmic decre- 

^ Of course, the same is not true of the current of induction, which 
depends on the resLstance of the circuit. 

" In Bfaxwell*s sense; we might say "lines of magnetic force" in 
Faraday's sense ; see art. MAQMniSM. 

* Wiedemann, Bd. ii. $ 706. * Exp. Ret., 1709, &c, 1838. 

* Other investigators have sought for such effects, and some have 
aflirmed their existMice ; but there is no body of concurrent testimony 
on tilt point. * MaatbtuUmm,^ U 10 and 11, 1846. 



ment' of its oscillations carefully determined. This decrement, due 
to the friction of the air, &c., was found to be constant for different 
lengths of the arc of oscillation. The terminals of the suspended 
coil were next connected so that it formed a closed circuit, and a 
constant current was sent through the fixed coil. Induction cur- 
rents were now generated in the suspended coil, whose electrody- 
namio action constantly opposed its motion. It was found that the 
logarithmic decrement was still constant, but greater than before. 
Weber therefore concluded that the induct current at each instant 
was proportional to the velocity of the coil. Since the resistance 
does not vary, this is in accordance with the general law. 

Weber further showed that the induced current is the same 
whether it is produced by a current in the fixed coil or by a magnet, 
which exercises the saune electromagnetic action as that current on 
the satpended coil, when the latter is traversed by a current of 
unit strength. 

The electrodynamometer may also be used to demonstrate the 
e(^uality of the whole amounts of electricity which pass in the 
direct and inverse currents. If the induced currents from a 
secondary coil whose primary is being ''made and broken" be 
passed through both coils of the instrument, there will be a deflec- 
tion, since the action depends on the square of the current ; but if 
the induced current be sent through the suspended coil alone, and 
a constant current be sent throng the fixed coil, there will be no 
deflection, which shows that the quantities of electricitv passing in 
the alternate currents of the secondary coil are equal and of opposite 
sign. 

Felici (1852 and 1859) made an extended series of Felid. 
experiments on the laws of induction. He used null 
methods, and his experiments bear a resemblance in some 
respects to the electrodynamical experiments of Ampire. 
MsLxwell^ has given a summary of Felici's results. 

It is found, for instance, that the electromotive force of induc- 
tion of a circuit A on another B is independent of the material 
or section of the conductors, that it is proportional to the current 
in A and to the number of windings in B. The induction of A on 
B is the same as that of B on A, wncn the inducing current i is the 
same in both cases. Any portion of A or B may be replaced by a 
zig-zag portion, which nowhere deviates far from it. In pairs of 
circuits geome^cally similar, the electromotive force of inductioQ 
is propo^ional to the linear dimensions, and so on. 

If B be so situated with respect to A that starting or stopping a 
current in A produces no induced current in B, B is said to be con- 
jugate to A. There are an infinite numbei of such conjugate posi- 
tions of B ; and Felici shows that, if B l)e moved from one of these 
Pi into another P, very quickly, no effect is produced on the gal- 
vanometer. If B ue moved from P| to any position P (not a con- 
jugate position), the efl'ect on the galvanometer is the same as if 
the current i were suddenly started in A, B being in the position P. 

All these results are direct consequences of our general law, and 
indeed might be used as a foundation for it* 

In his later researches on electromagnetic induction Faia- 
(series xxvii. and xxix.), Faraday develops in consider- day's ex- 
able detail his ideas on the connection between the lines P^<>^8 
of magnetic force and the induced current, and gives in- ^^ 
creased precision to the experimental methods that flow 
therefrom. He points out the great value of methods, such 
as the use of iron filings, for exhibiting in a visible form 
the course of the lines of magnetic force. He also insists 
on the great use of a small moving circuit, which can be 
used to explore the magnetic field under circumstances 
which render the application of other methods impossible. 

The direction of a line of force may be determined in various ways 
by means of the moving conductor. Maxwell*^ gives four such 
ways : — (1) if a conductor be moved along a line of force parallel to 
itself, it will experience no electromotive force ; (2) if a conductor 
carrying a current be free to move along a line of force, it will show 
no tendency to do so ; (3) if a linear conductor coincide with a line 
of force and be moved parallel to itself in any direction, it will 
experience no electromotive force in the direction of its length; 
(4) if a linear conductor carrying an electric current coincide in 
direction with a line of magnetic induction, it will not experience 
any mechanical force. 

In these researches Faraday treats at considerable length Unipolar 
a case of the induction of electric currents, to which Conti- induo- 
nental writers have given the somewhat mysterious name**®"* 
of " unipolar induction." It belongs to a class of cases on 

' See art. Galvanomctkr. 

• Vol. ii. § 536 ; see also Wiedemann, Bd. IL $ 709. 

• See Maxwsll, /.& ^« Vol ii. f 697. 



78. 



ELECTBICITY 



[ELBCiBoxxomna nnHTcnoiL 



which tiiey have rightly dwelt as being in a eenee the 
reveTBe of the electromagnetic rotatioas. The foHowiDg 
theory of the phenomenon will make this clearer ;-^ 

Rafening bick to fignra 40, let AB be part of s coadacting cir- 
coit uraoged u there described, and let it be canned to more ia the 
dinction Pp. Then if E be the electromotlTe force in the circait 
in the direction AB, K the numbeiof lineaof force passing throngh 
the eiienit, f the angle through which AB morea (from X to Y) 
about OZ, we have, by oar general law, 

' df dt' 
tifN 



E.-% 



Kow, by Ampire'a theorjr, K = ^ > hence (p. 7») 

" i di 



m(coi3,- 



«0, +C0fla,) -j 



(27). 



Hence, if the conductor AB be caused to move with given 
sognlar velocity about the magnet SN', in that direction 
which it wonhl take ncder the action of the magnet if it 
earned a current t, then there nill be an electromotiTe 
force of induction along the circuit of which AB forma part, 
whose direction ia opposite to that of i, and whose magni- 
tode ia found by dividing the couple acting on AB (when 
traversed by i) by t, and multiplying it by the given angu- 
lar Telocity. This result is a beautiful instance of the law 
of Lenz. 

A great variety of experimental arrangements may be 
imagined to realize the case thus described. Every appa- 
ratus devised to produce an electromagnetic rotation may 
be used to illustrate it 

The following caie may b« taken u tntical. SN (fig. K] 
magnet whose action may be lepreseoted by two polei, n and S. 
At the middle point of its aiii is Eied a disc 
BA, agaicit which presses the terminal of a 
wire CA in metallic connection with the iiis 
through the pivot at S. If CA be caused to 
rotate in the direction of the arrow p, the disc 
standing still, there will be an induced uuirent 
in CABC in the direction of the arrow q. If 
CA and the disc revolve together, there will 
be no canent If CA stand still, and the di<ic 
rotate in the direction of the arrow, th«re will 
be a current in the opposite direction; for thta 
is clearly the same as if the disc stood still, and 
CA rotsted in the opposite direction.' The 
electromotive farce in each case ia iodepen- 
dent of the form of CA, andii given by 
Sni(l -cosa)H, where m is the strength of the 
pole N, a the angle ANB, and m the angular 
Telocity. 

It is well to remind the reader that the lines of force are closed 
carves, every one of which pssses up the axis of the magnet from S 
to N, and back through the outside medium to S. If this be for- 
gotten, and an attempt be made to determine the electromotive 
nrce of induction by conatdering the motion of the disc, an error 
will easily be made. If we take the simpler course above, and 
consider the motion of the conductor, there is then no danger of 
miatake. 

(<0Us In most of the experiments we have hitherto been de- 

with iron scribing, the object has been to obtain indications of the 
*""• direction of the currents of induction, or to measure the 
electromotive force of induction under definite circum- 
stances ; if, however, we desire to exhibit the effects of 
induction in a striking manner, in order to convey belief 
to the spectator, or to serve some practical purpose, recourse 
is had to a different kind of apparatus. We may wind our 
primary and secondary coils on bobbins, and insert the 
former within the latter, so as to get the greatest possible 

* If the leader wish for a proximate rule for the direction of the 
•lectiomotive force of indaction, the following will serve. Stand with 
the body in the line of magnetic force with the head pointing in the 
poeitlve direction, look io the direction In which the part of the 
drcnit on which the feet are ii movlag ; the £. U. F. aloDg the circuit 
Is towards the rifiht hand. 




Fig. rt. 



number of tnma of wire into proximity. The nnmber of 
turns on the primary lb usually made small, in order that 
the current iu it may not be weakened by a large resist- 
ance, and that its coefficient of self-induction (see below) 
may be small. Mention has already been made of the 
effect of soft iron in increasing the number of lines of force 
that pass through a circuit. It is easy to see that it will 
produce a corresponding effect in stcsngthening induction. 
The precise amount of it is very bard to calculate, owing 
to the irregularities iu the magnetization and demagnetiza- 
ttOD that arise from reaidnal magnetism. The question 
belongs, however, to magnetism. The eff'ect can be de- 
monstrated practically by observing the alteration in the 
inductive action produced by inserting a bundle of iran 
wires* into our primary coLL 

The physiological effects of indnced cnmnts are verypbjiie- 
striking ; indeed, the nerve and muscle preparation of the hi^ 
physiologist affords a very delicate method for detecting *^''^ 
them If the human body form part of the drcnit of the 
secondary coil of such an induction apparatus as we have 
just indicated, and the primary current be stopped and 
started in rapid succession, say by stripping one terminal 
of the circuit on a toothed wheel attodied to the other, a 
sensation ia experienced which, with a moiientely powerful 
apparatus furnished with a core, is so painful and peculiar 
that the patient is not likely to forget either it or its came. 
The tetanic muscular contractions produced in this way 
have formed the subject of much physiological investiga- 
tion, of which an account will be found in the proper 
place (sea article Pbysiolooy). 

The flat spirala of Henry, formed of flat buids of copper 
insulated from each other with silk ribbon, are also very 
convenient for demonstrating the existence of induced 
currents. 

The most powerful inductive apparatus for furnishing 
large quantities of electricity are the various magneto- 
electric machines which have now been brought to great 
perfection (see Historical Sketch). 

By means of these and aimilor appliances, all the afleets 
of the electric current and the electric discharge may be 
shown in the greatest perfection. 

Induction by Diieharge of Statical Eleetrieitg. — ^The Indse- 
phenomena of induction can be exhibited with the tian- ^^^ 
sient current of electricity in the discharge of a Leyden jar ^^ 
or other accumulator of statical electricity. There ia Behnia 
difficulty in exhibiting the effect, owing to the great diflas 
ences of potential between different parts of the dremt, 
which render the application of a coil of silk-covered wir» 
useless. A common way of getting over the difficulty 
consists iu cutting tivo spiral grooves in two flat ebonite 
discs. Wires are embedded in these, and they are then 
put together with a thin plate of glass between, so that 
the spirals are opposite each other. When a jar is 
discharged through one spiral, an induction current passes 
in the other, and may be indicated by a galvanometer, or, 
better still, by a frog preparation. The indnced current 
is, however, in general a complicated phenomenon, owing 
to the oscillatory nature of the discharge (see above, p. 65). 

It would lead us too far to go into these and Undred 
subjects : the reader who desires to pursue the matter will 
find excellent accounts in Mascart, t. ii. §§ 611-825, and 
Riess, Bd. ii. §§ TSO-906. Particularly interesting are the 
researches of Verdet, an account of which will be found in 
his works, along with many indications of what others 
have done in the same field. 

Induced Currents of Higher Ordert. — Indnced cnrrenis 
may in their turn indnce other currents, and these again 



KLlCTEOMAOKSnC nn>UOTION.] 



ELECTRICITY 



79 



•d others, and so on.^ This can be brought about by forming 
tts part of the secondary circuit of one inductive apparatus 
^^^ into the primary of the next, and so on. As may be 
^ supposed, the successive induced currents diminish very 
rapidly in strength, and require special means for their 
detection. But the phenomenon also goes on increas- 
ing in complicacy. Suppose we start the current in the 
first primary, there is a single inverse current of the 
'' first order " which rises and then falls ; there will, there- 
fore, be two currents of the " second order " — firat a direct, 
then an inverse; each of these rising and falling causes 
two currents of the third order, and so on in geometric 
progression. These currents have been detected in certain 
cases by means of their physiological action and their mag- 
netizing powers. The latter effects present some points of 
interest in connection with magnetism, but we cannot spare 
space for the matter here. 

Self-Induction, — The existence of self-induction has been 
deduced as a theoretical consequence of the general law of 
induction. It was not so discovered, however. It was 
first arrived at by Faraday ^ from experimental considera- 
n't iions. The observation from which he started was the 
^^ following fact communicated to him by Mr Jen kin, who had 
shortly before discovered it : — Although it is impossible 
with a short circuit of wire and a single battery cell to 
obtain a shock by making and breaking contact, yet a very 
powerful shock is obtained if the coil of an electromagnet 
be included id the circuit. This may 
be shown thus :— Let ZC (fig. 50) be ^1 
a battery of a single cell, CABDEF a ^l 
circuit with a cross branch BF, in which 
at the human body, <kc., may be in- 
serted. Contacts can be made and 
broken at A, very rapidly if need be, by 
means of a toothed wheel When BDEF 
consists of a short single wire, nothing 
particular is felt at Q, but when the coil ^j 
of an electromagnet is inserted in DE, 
the patient at G experiences a series of 
powerful shocks comparable to that obtained from the 
secondary coil of an inductive apparatus in the manner 
already described. 

If the cross circuit be done away with, a powerful spark 
is obtained at A on breaking contact, but none on making. 
^^ This spark is particularly bright if a mercury contact be 
used, owing to the combustion of the mercury. If, how- 
ever, the electromagnet be removed from DE, and a short 
wire substituted, the spark becomes quite insignificant, al- 
though the whole circuit may be now very hot, owing to 
the increased current. Faraday found that the same effect, 
only smaller, was produced when a simple helix without a 
oore was substituted for the electromagnet ; and a similar 
effect, only still smaller, was obtained when a very long 
straight wire was used. Faraday soon recognized that 
these effects are consequences of the laws at which he 
had arrived in his first series of researches on induction. 
When the current is rising in a circuit, the number of 
lines of magnetic force passing through it is on the increase, 
hence an electromotive force is generated which opposes 
that of the battery, and causes the current to rise slowly; 
again, when the current begins to decrease the number of 
lines of force begins to decrease, and an electromotive 
force of induction is called forth which tends to prolong 
the current. We have, therefore, a weakening of the 
electromotive force at starting and an exaltation at stop- 
ping, which accounts for the absence of the spark or shock 
at make, and the presence of one or other at break. Such 

' Some phyridsti have called these currents indnoed coireDtB of the 
seoosd and third orders, kc 
* Bxp, Ret., 1048, kc.^ 1834. 




Fig. 60. 



inductive effects are obviously heightened when tiie cur- 
rent is wound into a spiral form ; if, however, the spiral 
were wound double, and the current sent through the two 
wires in opposite directions, the inductive effects would 
annul each other, and, in fact, with this arrangement the 
spark and shock are extremely small. 

Faraday demonstrated the existence of these electromo- His ez- 
tive forces by means of the currents which they produce peri- 
in derived circuits,' when the battery contact is broken "^®^*'' 
or made. 

He used the arraneement given in fignre 60. A galvanometer 
was inserted at G, and the nc^e stopp^ by pina properly plaG»d 
from deviating as urged by the brancn of the battery current from 
B to F, but left fr^e to move in the opposite direction. It was 
found that the needle deviated sharply wnen contact was broken at 
A, in a direction indicating a current from F to B. Again the con- 
tact was made, and the needle stopped at the deviation due to the 
current from B to F, so that it could not return to zero. The contact 
was then broken and made again, and it was found that at the make 
the needle tended to go beyond the position due to the steady current 
in BF. Faraday also arranged a platinum wire at G, so that it did 
not glow under the steady current in BF, but immediately ignited 
when the contact at A was broken. Chemical action was produced 
in a similar manner. In fact we may, by taking advantage of the 
self-induction, cause a sinsle cell to produce decomposition of water 
and evolution of gas, whidi it could not do alone consistently with 
the conservation of energy. This may be managed^ by inserting at 
A (fig. 50), instead of the contact breaker, the coil of an electro- 
ma^et, and placing the decomposing cell in DE. Let contact be 
made and broken at G (say by an automatic break) ; when the con> 
tact is made the current flows through the coil and through BF, 
when it is broken the electromotive force of induction added to 
that of the battery enables the current to pass through the cell and 
liberate the ions. At the make there is no such effect; there 
results therefore continued chemical decomposition. 

Edlund^ investigated the integral electromotive forces of Edlund't 
self-induction at the opening and closing of a circuit, and measure- 
showed that they are equal His experimental arrangement ^^ ^^ 
is very ingenious :— cunent. 

G (fig. 51) is a differential galvanometer, A a coll whose self-in- 
duction is to be examined, C a wire wound in a zig-zagf so as to 
have no self-induction. The battery 
E is connected at B and D with the 
circuit composed of G, A, and 0, so 
that the currents in BoiCD and 
B6aAD pass roimd the coils of G in 
opposite directions. The resistance 
is so arranged that there is no deflec- 
tion of the needle in G. If now the 
current be stopped by breaking the 
circuit EB atK, tne electromotive force 
due to the self-induction of A causes 
an extra current to flow round the 
circuit Aa6BcdCD, traversingthe coils 
of G in the same direction. We there- 
fore get a deflection D^ . In a similar 
manner if we make contact at K wo 
get another deflection D„ due to the 
starting of the current in A. There 
is no difficulty in showing that, if E|, 
£, be the time integrals of the electith 
motive force in the two cases, then 

E -D,- 




Fig. 51. 



One of the difficulties encountered in such experiments 
is the increase of the electromotive force of the battery E 
when it is left open for a time ; this causes the extra cur- 
rent at make to be greater than that at break. Rijke, who 
made experiments similar to those of Edlund, avoids this 
difficulty by circuiting the battery, when BK is broken, 



' These currents are sometimes called extra currents, and the name 
is applied even when there is no alternative circuit. The extra cor- 
rents are then the defect or excess of the currents at the make and 
break, considered with reference to the steady current. 

* De la Rive, Wiedemann, Bd. u. § 740. 

» Pogg. Ann., 1849. 

< The beet arrangement would be to use insulated wire and double 
it on itself. 



80 



ELECTRICITY 



[blectsomaonbtio iNDuonov. 



through a resistance equal to the effective resistance from 
E to K. Further details concerning the method and results 
of these experiments may be found in Wiedemann, Bd. il 
§ 744, &c. 
Max- A very convenient method for exhibiting and measuring 

well'i the extra current is obtained by using a Wheatstone's 
method, ^j^dge instead of a differential galvanometer. Let the 
bridge be balanced as usual, so that when the battery 
circuit is made, and the galvanometer circuit made after- 
wards, there is no deflection. If one of the resistances be 
wound 80 as to have a large coefficient of self-induction, 
and the galvanometer circuit be completed before the 
battery is thrown on, then, owing to the self-induction, the 
galvanometer needle will be suddenly deflected. 

Let AC, CD, DB, BA be four conductors of resistance S, Q, P, R, 
arranged as a Wheatstone's bridge (see fig. 22), with a battery be- 
tween A and D, and a ^vanometer G ^tween B and C. Let L 
be the coefficient of self -induction of the coil S. Then, A, C, &c., 
denoting the potentials at A, C, &c., x and y the currents in AC 
and AB, and z the current in G, we havo 

A-C=Sy+L^, A-B-Rr, C-D=Q(y+«), 

&c Eliminating, as in ^lazwell, vol. i. p. 399, or above, p. 43, 
we get 

ps-qr+pl4 

«= 1^7 E (28), 



D' 



d . 



where t> is a separated symbol, and D' is the determinant of the 

d 

system of resistances with S+^ written for S. We may there- 
fore write 

D being the ordinary determinant, and H a function of PQR, &c., 
which we need not determine. Equation (28) may therefore be 
written 



d.+hl^=pl^ 



(29), 



provided the bridge be balanced, i.e. if PS- QR be zero. Suppose 
now the cralvanometer circuit is closed, and then the battery cu'cuit 
closed ; then, inte^ting equation (29), from the instant before the 
battery is thrown in up to a time r when all the currents have be- 
come steady and no further current flows through the galvanometer, 
we get 



DJ zfltt-PLE, 



PLE 



or 



«i- 



where z^ denotes 



J zdt, i.e. 



D 



(30), 



the whole amount of electricity that 



flows through the galvanometer oi^ine to the induced current. If 
now we derange the balance in the bridge by increasing S by a small 
Quantity x, and decreasing Q by as much, we get a steady current 
tnrough the galvanometer given by 



s= 



Hence 



(P+R)xE 

D 

PL 



«""(P + R)x 



(81). 



Now, it fihe the first swing of the galvanometer needle, owing to 
the induction current, a the deflection under the steadv current, and 
T the time of oscillation of the needle under the earth's force alone 
(T is supposed to be so large that the duration of the induced 
current u very small compart with it) ; then it may be shown that 

2,__T8inJ/3 

X irtana 
Hence 

(P+R)ajT8inJ/3 



(32)J 



L-- 



Pirtana 



(38;. 



We thus ffet L in terms of quantities which can be easily measured. 
This methed of finding L is due to Maxwell. 

^ Certain corrections would ia general be necessary in practice, but 
we need not discusa them here. 



The application of the equations (26) to determine the Gdak 



bolti. 



march of the current in certain simple cases leads to results ^'JH^ 

of great interest. 

Suppose that an electromotive force E begins to act in a ciitnit 
of resistance R and coefficient of self-induction L. The equation 
for the current strength t at any time t after it has begun to act, is 



L^*+Ri=E 
at 

E. 



The integral of this is t — =(1 - « ' l *) 



(3i). 
(85), 



the constant of integration being determined by the condition 
i — ^( — steady current) when < — « , 

Hence the current starts with the value zero, and in- 

E 

creases continuously till it reaches the steady value ^• 

E ^t 
The part-tptf'^ is due to self -induction, and is called 

the extra current. The whole amount of electricity passing 
in this part of the current is 

- -^ . . .... (86). 

The quantity ^ is of the same dimension as t, and is TiatM 

called the time constant of the coiL According as the time a eoO. 
constant is greater or less, the longer or shorter time will 
the current take to rise to a given fraction of its steady 
value. If we desire therefore to prolong the induction and 
to increase it as well, we must make L large and R small, 
two conditions which in the extremes are inconsistent Cal- 
culations of the form of coil for maximum inductive effects 
might be made, but this is not the place to enter on them. 
Next, let the electromotive force E suddenly cease to 
act, the resistance of the circuit being unchanged. This 
may be realized experimentally within certain limits by 
throwing the battery out of the circuit, and at the same 
time substituting for it a wire of equal resistance. It is 
easy to show as above that the extra current at a time t after 
E ceases to act is 



E -»i 



£L 



and the whole amount of electricity which passes is + ^^ . 

Helmholtz,^ who was the first to treat this subject both Ezpcri- 
experimentally and mathematically, operated as follows : — ""*"*■ ° 

(1) The battery was thrown into the circuit, and after a time t the }^qI^ 
circuit was broken. 

(2) The battery was thrown in, and after a time t replaced by a 
circuit of equal resistance. 

These changes were effected by means of a system of levers, 
which it is not necessary to describe here. An account of the 
apparatus will be found in the paper quoted. 

The amount of electricity which passes through the circuit ii 
measured by a galvanometer whose time of oscilla&on ia long com- 
pared with i. In the first case the amount la 



in the second 



, E< EL/, -?«\. 



H^' 



because here the two extra currents just counterbalance each other. 

The observed value of B in each case enables us to calculate t. 
E and R being found by separate observations, one obeerved value 
of A enables us to calculate L. Using these values of £, R and L, 
a series of values of t, and hence A, can be calculated from the 
observed values of B, and the result compared with the observed 
value of A. The agreement between theory and experiment was 
sufficiently close to justify the application of the principles from 
which the above formula were deduced. Among these piinciples 
may be mentioned the validity of Ohm*s law for transient cuirents. 

The reader will find in the original paper details conoeming the 
above and other similar results arrived at by Helmholtz. 

' Po^. Ann,f 1851 



XLlOTBOlCAOinRIO INDUOTIOK.] CLCGTRICITY 



81 



>flzed The case of two circuits of invariable form and position 
■^ is of great interest, from the light it throws on the action 
of the induction coiL We shidl suppose that we have no 
soft iron core, and that the break in Uie primary is instan- 
taneous. The latter condition is very far from being 
realized in practice, even with the best arrangements, so 
that our case is an ideal one. 

Let t and j be the carrent strengths in primaiT and secondary, 
B and S the resistances, L, M, N the coefficients of induction, £ the 
dectromotiye force in the primary. The equations are 






(87), 
(38). 



It Is easy, in the first place, to show that the whole amounts of 
electricity which traverse the secondary at make and break of 
the primary are equal but of opposite signs. In fact, if we integrate 
(88) from the instant before make to a time when the induction 
currents both in primary and secondary have subsided, we get 



/ 



.,, M, ME 



(89). 



where 1 denotes the steady current in the primary. Similarly inte- 
grating over the break, we get 



/> 



^ 8 SR 



In the second place, if we assume the break instantaneous, we can 
find Uie initial value of the direct current in S. Thus integrate^ 
(88) from the instant before break to the time r after it, r being 
infinitely short compared with the duration of the induction currents, 
then 



-Mi+Nyo+s/Gvtt-o. 



Kow the last term may be neglected, because r is infinitely small 
andy ii not infinite, hence we &ve, for the initial value of^. 



a1| ^i!< 



(40). 



It is yery easy now to determine the farther course of the current 
in 8. llie equation for/ reduces to 



and we get, using (40), 



N*+%-0 ; 
. ME^-lt 



(41). 



The direct induced current (current at break), therefore, 
starts in our ideal case with an intensity which is to the 
intensity of the steady current in the primary as the 
coefiicient of mutual induction of the coils is to the 
ooefiident of self-induction of the secondary, and then dies 
away in a continuous manner like any other current left to 
itself in a circuit of given resistance and self-induction. 

Since we have already given enough of these calculations 

to serve as a specimen, we content ourselves with stating the 

result for the current at make. Owing to the self-induction 

of R, kcy the current in R rises continuously from zero to 

the value I ; the induced current in S therefore begins also 

from zero, rises to a maximum, and then dies away. The 

mathematical expression for it contains, as might be expected, 

tvoo exponential terms. 

Ql,^ It is instructive, in connection with what has already been 

•He said concerning the electrokinetic energy of two moving 

■ST* circuits, to examine what becomes of the energy in the case 

of two fixed circuits of invariable form. 

Equations (87) and (38) mav be used if, for generality, F be 
written instead of in (88), so that there is electromotive force (say 
of constant batteries) in both circuits. Multiplying (87) by i and 
(88) by y, adding, and integrating from the time before E and F begin 
to act to a time r when the currents have aU become steady, we get 



^ The reader might suppose that this proceu of integration might be 

Sually aimlied to (87). This is not so, however, owing to the vari- 
Uity of B at the brnk. 



y^rE»-R»«)^4/7F>-l5;'»)rf^-i(Lt«+2Mv-»-iy«) . (42). 



In words, the excess of the chemical energy exhausted in 
the batteries over the amount of eneigy which appears 
as heat in the circuits is J(Li*-h2M(; + H;"^), which we 
denote by K. Similar remarks to those made at p. 76 
apply here. K is the amount of electrokinetic energy 
stored up in the medium surrounding the circuits during 
the time that £ and F are raising the currents against self 
and mutual induction. 

If we integrate similarly over the break of both currents, 
we find the defect of the chemical energy exhausted under 
the heat evolved in the circuit to be again K. Much of tht 
energy thus discharged from the system at break usually 
appears in the spark. 

Electrical Oscillations. — Helmholtz^ seems to have been Electri- 
the first to conceive that the discharge of a condenser might ^ <'*^* 
consist of a backward and forward motion of the electricity ^***'"** 
between the coatings, or of a series of electric currents 
alternately in opposite directions. Sir William Thomson ' ^°"^* 
took up the subject independently, and investigated mathe- theory, 
matically the conditions of the phenomenon. 

Let q be the charge of the condenser at time <, C its capacity, 
E the difference of potentials between the armatures, t the current 
in the wire connecting the armatures, R its resistance,^ L the co- 
efficient of self-induction. Then we have 



and 



».«., 



L^+Ri-E. 
ePq R<fo 1 



The solution of this equation is 

g=^-*«(A««'+B<r-*0, . 



(48). 



(44), 



where 



m 



R ^ /R« JL 
"2L' V 4L?""LC 



A and B are constants to be determined by the conditions 
^-Q and ^=0 when t-0. 

Two distinct cases arise. 

(1.) Let R be greater than /^;thenthecxponentiabin(44) 

are real, the discharge is continuous, all in one direction, and in* 
volves no essentially new features. 

(2. ) Let R be less than / -— - ; then the appropriate form of Uie 

solution is 

g-«""** (A cos n/ + B sin n/), 

whe re m has the same meaning as before, but n stands now for 

"i R* 

=-T^ - -jy-j . If we determine A and B by the initial conditions, 

we get y-«-^/^cosn/+^sinn/)Q . . . 

The current is given by 



wuer 



(*6). 



•-File 



sin rU, 



(it,). 
iZ 



It follows from these equations that, when R K^j^ -ft i the 

charge of 'one armature of the condenser passes through a series of 
oscimitions. The different maxima are 



Q, 

occurring at times 
0, 



Mir 



Q< 



» » 

2t 



Qtf'V", &c, 



?5,&c. 
n 



* Die Erhaltung der Kra/t, 1847. 

* Phil. Mag., 1855. This paper is a very remarkable one in many 
respects. The methods used in the beginning to arrive at the equation 
(43) are well worth the reader's study. 

* R here mast be understood to represent the mean resistance ai 
the circuit during the discharge. 

vm — II 



ELECTKICITy 



[sLEOtBOItOnTB iMooonost, 



Wban the chwge has any of tbsw maiimmii values, the carMnt ia 
nto. The cnmnt maxima form a aumiar deacending geometrio 

fl+2, e + 3^ ^„ 



wbere 9 U the acnte angle tan ^. 

Tha interral between taj poaitive and the next negatire maii- 
Bom, whether ot charge or current, ia therefore - . 

We need not inabt on tlie evident importance of this 
result Thomson, in Ms original paper, points out the 
various applications of which it is capable. He predicts 
the phenomena afterirards observed by Feddersen ; in fact, 
he suggests the use of Wheatstone's mirror to detect it. 
Its bearing on the anomalous -magnetization of steel needles 
by jar discharges, and on the anomalous evolntion of gas 
b; statical discharges, when electrodes of email surface are 
used (in WoUaaton's manner), are also dwelt upon. 
Biperi- Several physicists have taken up the experimental in- 
ments ol vestigation of this matter. Feddersen's experiments realize 
'^^' the case above discussed, if we abstract the disturbance 
""^ owing to the air interval, of the effect ot which it is not 
easy to give an accurate account. Feddersen's results are 
in good general agreement with theory. He finds, for m- 
stance, that the critical resistance at which the discharge 
begins to assume the oeciUatury character variee inversely 
as the square root of the capacity of the battery from which 
the discharge is taken. A good account of the researclies 
of Paalzow,' Bernstein,' and Blaserua, and of the older 
researches of Helmholtz,^ remarkable for the use of his 
pendulum intermptot, will be found in Wiedemann, §§ 801, 
&a. Schiller, in a very interesting paper,* describes a 
variety of measurements of the period of oscillation, and 
the damping of the alternating currents in a secondary 
coil, when the current of the primary is broken. By means 
of the pendulum interruptor of Helmholtz (for descrip- 
tion of which see tus paper) the primary is broken, and at 
a measured interval thereafter the secondary circnit, which 
contains a condenser and a Thomson's electrometer, is aisc 
broken. The deflection of the electrometer indicates the 
charge of the condenser at the instant when the eecondarj 
is broken. The interval between two null points sepa 
rated by a whole number of oscillations can thus be found, 
and hence the time of oscillation of the coil calculated. 
The agreement of Schiller's results with calculation is verj- 
remarkable, and must be regarded as a highly satisfactory 
proof of the validity of the theoretical principles involved, 
T^fln^ Indin:tum in Matteg 0/ Mttal and Magnetimn of Rota- 
tion in tion. — Hitherto we have dealt only with linear circuits ; 
nuuaaotbut it is obvious that currents will also be induced in a 
'"*'''■ mass of metal present in a varying magnetic field. If the 
variation of the field be due to relative motion between thi: 
mass of metal and the system to which the field ia due. 
the electromagnetic action of the induced currents will 
oppose the motion. Many instances might be given of 
this principle. If a magnet be suspended over a coppei 
disc, or, better still, in a sroall cavity inside a mass oi 
copper, its vibrations are opposed by a force due to thi- 
induced currEuta which for small motions varies as tht 
angular velocity of the needle. Accordingly, it come^, 
much sooner to rest than it would do if suspended in the 
air at a distance from conducting mosses ; it moves besidi. 
the copper as if it were immersed in a viscous fluid. 
Eipari- Plilcker suspended a cube of copper between the poles of ,1 
meat! or powerful electromagnet, and set it spinning about n 
Plilcker vertical axis ; directly the magnet was excited it stoppeil 
^j^""' dead, Foucault arranged a flat copper diac between thi' 



dat poles of an electromagnet placed at such a diatance 
apart as just to admit it between them. The disc was aet 
in rotation by means of a driving gear. So long as the 
magnet was not excited, the driver bad comparatively little 
work to do ; but as soon as the magnet was excited, die 
work required to keep up any considerable velocity greatly 
increased. The additional work thus expended appeara in 
the heat developed in the disc by the induced curraota. 
Tyndall demonstratea this very neatly by causing a small 
cylindrical vessel of thin copper filled with fusible metal 
to rotate between the poles of an electromagnet, when 
Luough heat is quickly developed to melt the metaL 

On the other hand, when a mass of metal moves in the Angt'i 
neighbourhood of a magnet, the electromagnetic action of "P*^ 
the induced currents will cause the magnet t» mova, if it ""^ 
l>e free to do so. Thus, if we suspend a magnet with ita 
iixis horizontal over a disc which can be set in rotation 
about a vertical axis, owing to the electromagnetic action 
i)f the induced current, the needle will tend to rotate in 
the same direction as the disc. If the velocity be great 
imough, or the needle be rendered astatic, it may be 
iiarried round and round continuously. Thia action was 
iliscovered by Arago, and excited the attention of many 
philosophers, till it was at last explained by Faraday (see Fan- 
Historical Sketch). Many of the observations made bydiji 
faraday's predecessors, and some made by himself, are at ^^ 
once seen to support the couclnsion that the pheoomenaa 
Is simply a case of Lena's law. Thus Snow Hairia foBnd 
that the deflecting couple on a suspended needle varied 
approximately as the velocity of the disc directly, and as 
the square of the distance of the needle from the disc in- 
versely. It was also found that the action of the diac woa 
directly proportional to the conductivity of the metal of 
which it was made, an exception occurring in the case of 
iron, whose action was disproportionately great. Cutting 
radial slits in the disc diminished the action very rnnch. 

Besides the component tangential to the disc, it ia fomid 
that there is a repulsive normal action on the pole of the 
magnet, and also a radial action, which may be towards or 
from the centre of the disc, according as the pole ia nearer 
or farther from the centre of the disc These acti<ms look 
at first sight somewhat mora difficult to explain; but a little 
consideration will show that the laws of induction account 
for these alsa 

Let UB ftrat suiipose the induced enrreuta to appear and die away 
inatiiutJy after the small motion of the disc whidi ppedocea dtrm 
(we maif suppose the motion of the disc to take place by an '"*■'''» 
number of small jumpa). Thus the currents of induction are 
obviaual J a jmmetrical with reapect to the diameter through the foot 
of the perpendicnlar boia the magnetic pole on Qie disc, and we 



a perjiend 
rouohly 







trotUBf^uetii 

tion by a mainict 

placed perpendicu- 

tiuice from the 
centre of the disc, 
ita south pole poin t- 
ing in the direc- 
tion of the diac'a 
motion if the 
during pole I 
north po[e. 
UX(fi^.52i belli 

Fig. 6a 

same vertical iilana as the pole, IfS the rtpresentadva magae^ 
OY bi'ing the direction of motion. By our present auppoaitioa ttaa 
inducing pole M lies in the plane of ZOX, in which eaae It to 
obvious that the resultant action reduces to a tangential cann- 
-' ■ ponent T jiarallel to OY. 

~ J But, owing to the indactive acttoc on each other of the cnmntt 
I in the disc, the induced cnrrenta do not riae and (all inatan- 
I taneoosly, bat endure for a aenaible tune. Tyirmarrnnrrhljiiiijl— t 



BSaOTBOMOTlYS fOBOS.] 



ELECTRICITY 



83 



tlM effect of tkU by anpposing the repreaentatiTe magnet NS 
carried onwards a little with the disc, or, which amounts to the 
•ame thing, we may suppose the pole M to lag a little behind at 
IT (lying, say, on MM7 perpendicular to ZOY.) The action of N 
will now preponderate, and the resultant force on M' will be in the 
direction M'F. This force, when resolved parallel to OY, OZ, OX, 
gires a tangential component as before, a repulsive normal com- 
ponent, and a radial component, which will be directed to or from 
the centre of the disc, according as the representative magnet lies 
farther from or nearer to the centre of the disc than the foot of the 
perpendicular from M'. 

The original explanation of rotation magnetism (Faraday, 
JSxp, lies., 81, Ac.) should be consulted by the reader who 
widies to pursue the subject. An account of the researches 
of Nobili, Matteucci, and others will be found in Wiedemann, 
Bd. iL § 860, &c. The mathematical theory has been 
treated by Jochmann, who neglected the inductive action 
of the currents on each other (Crell^t Joum., 1864 ; 
Fo^^. Ann,, 1864; also Wiedemann, /.c). A complete 
theory of the induction of currents in a plane conducting 
sheet has been arrived at by MaxweU by means of an 
extremely degant application of the method of images 
(Proe. RS.J 1872 ; also ElectricUy and Magnetism, vol 
IL §§ 668, 669). 

On the Origin cf Electromotive Force. 

It remains for us now to view the transformations of 
energy which take place in the voltaic circuit from the 
other side, and to inquire whence comes the energy that is 
evolved in so many different forms by the electric current. 
Two distinct questions are here involved. First — ^What 
form of energy is being absorbed, and at what part of the 
circuit does the absorption take placel Secondly — Where 
18 the electromotive force which drives the current situated 1 
^^ To the first of these questions experiment has given, on 
Q of the whole, a very satisfactory answer. The electric circuit 
(y. 10, indeed, one of the best instances of the great law of 
conservation, which states that the appearance of energy 
Anywhere is always accompanied by the disappearance 
somewhere of energy to an equal amount. No general dis- 
cussion of this first question is necessary; it will be suffi- 
cient to indicate the application of the general principle 
when we deal with particular instances. 

Unfortunately the answers, both experimental and 
theoretical, that have been at different times given to our 
second question, are not so concordant as could be desired. 
The reader is, therefore, cautioned against accepting with- 
out due examination^ anything that may be here advanced. 

Perhaps the most general principle concerning the 
origin of electromotive force recognized by physicists of 
the present day is the following: — 

When ttvo different substances are in contact, there exists 
in general an dectromotive force at the surface of separation, 
tending to displace electricity across that surface. 

This electromotive force is commonly called the ** electro- 
motive force of contact," or simply the " contact force." In 
the particular case of two conductors in contact, the effect 
of this force would simply be to maintain a certain differ- 
ence of potential between them. 

Although the earliest known case of electrification — viz. 
amber rubbed with woollen cloth — is an instance in point, 
and although many experiments on electrification by the 
friction of different substances were made, yet this prin- 
ciple was not recognized fully till the experiments of 
Oalvani and Yolta directed the attention of men of science 
to the matter. 

Yolta was the first to demonstrate clearly the existence 
of the contact force in the case of metals. A simplified 
form of his fundamental experiment is the following. The 



act 



act 



la. 
ft't 

ti- 



' This applies particularly to any indications of the Tiews of tiring 
pbyiiditB. 



upper and lower plates of a condensing electroscope (see 
above, p. 34) are made of different metals, say copper and 
zinc Let the upper plate be laid upon the lower, and the 
metallic contact ensured by connecting them for an instant 
by means of a wire. If the upper plate be now lifted verti- 
CiiUy upwards, the gold leaves of the electroscope diverge, 
indicating that the zinc plate is now positively electrified to 
a considerable potential This is explained as being due to 
the contact force at the junction of the copper wire with 
the zinc plate, by virtue of which the zinc is at a higher 
potential than the copper. Suppose the upper plate to be 
connected with the earth, then if £ be the contact force, 
the potential of the zinc plate is E. Now E is very small, 
but as soon as the upper plate is ndsed the potential of 
the lower plate is increased in the same ratio as its capacity 
is diminished; hence the divergence of the leaves. Yolta Law of 
found that he could arrange the metals in series, thus — Yolta. 



Zn 

Pb 



5 

1 


Fe 


1 
2 
3 


Cu 


Sn 


Ag 





such that, when any metal is placed in contact with one 

below it in the series, it takes a higher potential ; and he 

found that the electromotive force between any two metals 

in the series is the sum of the electromotive forces between 

every adjacent intervening pair. Thus, if ZnlPb denote 

the electromotive force from lead to zinc, we get from the 

above table, 

Zn!Pb=5,Pb|Sn=l, 
ZnSn = ZnlPb + PblSn = 6, 
Pb|Cu=PblSn + Sn|Fe + Fe|Cu=6, 

and so on. 

It follows from Yolta's law that, if a number of metale 
be connected up in series, the difference of potentials be- 
tween the extreme metals is independent of the intermediate 
metals, and, in particular, is zero if the extreme metals be 
the same. We cannot, therefore, have a resultant electro- 
motive force in a closed circuit consisting of metals merely. 
This is entirely in accordance with experiment, provided 
the temperature be the same everywhere. 

While one party of physicists neglected or attempted to 
explain away Yolta's contact force, another took up the 
investigation, and endeavoured to obtain precise measure- 
ments of it in different cases. Careful experiments of this gj^j^. - 
kind were made by Koblrausch* and Gerland,^ by a method ments by 
due to the former. Kohl- 

A condenser is used whose plates are made of the metals »a«cb. 
to be tested, say zinc and platinum. The plates are first 
placed parallel to each other at a very small distance apart, 
and touched simultaneously with a wire (say of platinum). 
A difference of potentials is thereby established, so that if 
the potential of the Ft be zero that of the Zn is Zn|Pt. 
(Here we neglect the contact force between air and 
zinc and between air and platinum. No experimental 
proof that we know of has been given in support of this, 
see below, p. 85). In consequence of this difference of 
potentials the Zn plate becomes positively charged. The 
wire is now removed, the plates of the condenser separated 
to a considerable distance, and the Zn plate connected with 
one electrode of a Dellmann's electrometer, the other elec- 
trode of which is connected to earth. The reading is pro- 
portional to the potential difference ZnlPt increased in 
the ratio in which the capacity of the Zn plate has been 
decreased by the separation. Hence, if A be the reading, 



Zn|Pt-\A 



(1). 



The condenser plates are now brought into their former 
position, and connected through a Danieirs cell, consisting 



• Pagg, Ann,, 1868. 



* Pogg. Anm., 1868^ 



84 



ELECTRICITY 



[ELBOTBOMOnTB FOBC& 



of a strip of zinc immersed in a porous vessel filled with 
zinc sulphate, which is itself immersed in a vessel containing 
copper sulphate, into which dips a strip of copper. In the 
first instance, the copper strip is connected with the zinc 
plate, and the zinc strip with the copper plate of the con- 
denser. The difference between the potentials of the con- 
denser plates is easily found by an application of Yolta's 
law^ to be D + Zn|Pt, where D denotes the difference 
between the potentials of the two pieces of copper forming 
the terminals of a Daniell's cell ; hence if B be the electro- 
meter reading, after removing the Daniell and separating 
the plates as before, we have 

D + Zii|Pt=xB (2). 

If we connect up the Daniell the opposite way with the 
condenser, then we get a reading C, such that 



D-Zn|Pt-xC 
From (2) and (3) we get 

Zn|Pt.|^D 



(3). 



(4), 



which gives the contact force ZnjPt in terms of the 

electromotive force of a Daniell. From (1), (2), (3) we 

get 

B-C-2A, 

an identical relation which the observations ought to satisfy, 
and which, therefore, affords the means of testing their 
accuracy. 

In this way Eohlrausch found for Zn|Cu the value '48D , 
or in other words, that the contact force from copper to zinc 
is about equal to half the electromotive force of a Dani ell's 
ceU. As an instance of the general nature of the results, 
we give two series of numbers from the observations of 
Eohlrausch. The contact force is between zinc and the 
metal mentioned in first column in each case, and Zn|Cu is 
taken » 100. 



Cu 

Au 


100 
112 
106 
106 
76 


100 
116 
109 
123 


Aff 


Pt 


Fe 


1 .. 



In the second set of experiments the metals were care- 
fully cleaned, whereas in the first set they may have been 
a little 02ddized. This may very well account for the 
differences, for Kohlrausch found oxidized zinc strongly 
negative^ to freshly cleaned zinc. In fact, he found 
Zn I ZnO = about •4Zn I Cu. 

In order to testVolta's law, a further series of observations 
was made, giving the contact force between iron and several 
metals. The following table gives the results observed 
directly and calculated from the table last given : — 





Obserred. 


Calculated. 


Cu 


81-9 
32-3 
397 
29-8 


25-3 
32-3 
38-0 
30-9 


Pt 


Au 



It will be seen that, with the exception of the values for 

FelCu, the agreement is very fair. 

Qerland It is not necessary to give here the results of Qerland 

and and Hankel.^ The latter made a great number of very 

Hankel. careful experiments. He showed that the results depend 

^ The truth of which, therefore, is assumed. The assumption of 
course is justified a posttriori, 

' A metal is said to be negative to another when it assumes the 
lower potential in contact, and positive when it assumes the higher 
potentiaL 

* AhK, der KSaigl Sdeha. QudUcKaJt, 1861, 1866. 



on the nature of the surface of the bodies, being different 
when the surface is filed and when it is polished with rouge 
or other powder. His tables also show the gradoal change 
effected in the contact force when the plates are exposed to 
the action of the air. 

According to Yolta, the contact forces between metals ^ 
and liquids are either very small, and do not follow the same ^ 
law as the contact forces between metals, or else are abso- 
lutely non-existent. Subsequent observers, however, de- 
monstrated the existence of contact forces in this case also, 
but showed that they do not obey Volta's law like the con- 
tact forces in the case of metals. 

Becquerel ^ placed the fluid to be examined in a capsule Bee 
of the metal, say copper. The capsule was placed on the ^ 
upper plate of a condenser consisting of two copper plates 
in connection with a gold-leaf electroscope. The fluid and 
the lower plate of the condenser were touched each with a 
finger for a short time, and then the upper plate was 
removed. The divergence of the gold leaves was taken to 
indicate the contact force. In this way Becquerel found 
that zinc, copper, and platinum were mostly negative to 
alkaline solutions ; but the metals were in general positive 
to concentrated sulphuric acid. It is obvious, however, 
that the result of the experiment is complicated by the 
contact of the hand with the liquid and with the metal of 
the condenser. 

Similar objections apply to the results of Pfaff^ and 
Peclet.« 

Buff^ made the lower plate of his condenser of the metal 
to be examined, of zinc for example ; upon this was laid a 
thin glass plate on which was spread a thin layer of the 
liquid to be examined, or a piece of filter paper soaked with 
it. A zinc wire was used to bring the liquid and the lower 
plate of the condenser into communication ; this wire was 
then removed and the glass plate with the liquid lifted. 
The divergence of the leaves was taken to indicate the 
contact force between zinc and the liquid. Although this 
method is an improvement on the methods of Becquerel 
and Peclet, it is still unsatisfactory, owing to the presence 
of the glass. 

The most extensive and at the same time most careful Hssk 
experiments at present on record are those of HankeL^ ™*'^ 

The fluid (L) to be examined was placed in a wide- 
mouthed funnel The condenser was formed by the surface 
of the liquid and a copper plate, which could be placed 
parallel to it at a very short distance apart, and raised as 
usual The stem of the funnel was bent at a right angle 
twice, and ended in a wider portion, into which dipped a 
strip of the metal (M) to be examined M was connected 
for a moment by a platinum wire with the copper plate 
and also with the earth. The wire was then removed, the 
plate was raised, and its potential determined by means of 
Hankel's dry pile electroscope. The reading (A) is pro- 
portional to Cu|Pt -H Pt|M -f MIL, or, by Volta's law, to 
Cu|M -f MIL. Hence 

Cn|M+M|L-xA. 
In the next place, the funnel is emptied and a plate of the 
metal M placed on its mouth. The copper plate is lowered 
so that it is at the same distance as before, contact estab- 
lished by means of the platinum wire, and so on. The 
reading being B, we have 

Cu|M=\B. 

The plate of M is replaced by a plate of zinc, and the 
experiment repeated, and we have, C being the third read- 
ing, 

Cu|Zn-xC . 



^ Ann.cUt Chim, et de Phys., 1824. ■ Pogg. 

• Ann. de Chim. et de Phys., 1841. 
^Ann, der Chetn. u. Pharm., 1842. 
*Abh.der. KGnigl. SOchs. QudUcKaft^ 1865. 



184a 



mOIXOMOTIVB fOBCn.] 

From these three reeolts we get 



ELECTRICITY 



85 



M|L-^^rCu|ZIl. 

It is not necessary to qaote Hankel's results here. The 
reader may refer to Wiedemann's OcUvanismtu, or to 
HankeFs paper. 
^ Sir William Thomson has given a new proof of the 
d»- existence of Yolta's contact force as follows.^ A ring is 
itrm- formed, one-half of which is copper the other half zina 
^ This ring is placed horizontally, and a needle made of thin 
sheet metal is so balanced as to form a radius of the ring. 
If when the needle is unelectrified it be adjusted so as to 
be over the junction of the two metals, then, when it is 
positively electrified, it will deviate towards the copper, and 
when negatively electrified, towards the zinc. Again, if a 
whole, instead of a half needle as above, be suspended over 
a disc made of alternate quadrants of zinc and copper, or, 
better still, inside a flat cylindrical box constructed in a 
similar way, so that when the needle is unelectrified its 
axis coincides with one of the diameters in which the disc 
is divided, then when the needle is positively electrified 
it will take up a position such that its axis bisects the 
copper quadrants ; if it be negatively electrified, its axis 
will bisect the zinc quadrants. 

Thomson has also given an elegant demonstration of 
the contact force between copper and zinc by means of an 
apparatus which is a modification of hb water-dropping 
apparatus.' A copper funnel is placed in a cylinder of zinc, 
and drops copper filings at a point near the centre of the 
cylinder. The filings are charged negatively by induction 
as they fall, owing to the excess of the potential of the zinc 
cylinder over that of the copper. If therefore the filings 
be caught in an insulated metal can, they will communicate 
to it a continually increasing negative charge, while the 
zinc cylinder and the copper funnel will become charged 
more and more positively. 

Thomson finds, in agreement with Kohlrausch, that, when 
the copper and zinc are bright, the electromotive force of 
contact is about half that of a Daniell's cell When the 
copper is oxidized by heating in air, the contact force is 
equal to a Daniull or more. He has gone a step farther, 
and shown that when two bright pieces of copper and zinc 
are connected by a drop of distilled water, their potentials 
are as nearly as can be observed the same.' 
ML The subject of contact electricity has been taken up quite 
recently by Clifton.'* He experiments on the contact force 
between a metal and a liquid by a method which is a 
simplification of HankeVs. 

Two horizontal plates are used of the metal M; the 
liquid L is placed in a glass vessel on the lower plate and 
connected with the lower plate by a strip of the same metal 
which dips into it The upper plate is lowered to a 
distance of 0*1 or 0*2 mm. from the surface of the liquid, 
which acts as the lower surface of the condenser, and the 
upper plate and lower plate are connected by a copper 
wire. The difference of potential between the two surfaces 
of the condenser is therefore M|L. The copper wire is 
then removed, the upper plate raised, and its potential 
measured with a Thomson's electrometer. In this way a 
contact force equal to the thousandth part of Zn|Cu can be 
detected. 

Clifton finds zinc and copper to be both positive to water 
to about the same degree, and both very slightly negative 
to dilute sulphuric add. He concludes therefore that zinc 
and copper dipping in water will be at the same potential 
This he verifies directly, finding that any difference of 

> Froe, Lit and PhO, Soc. qf ManeKester, 1862,or Reprint, p. 319. 

* Rtprint, p. 824. * Jenkin, BUctr, and Mag., % 22. 

* Froe, R, S^ Jona 1877. 



potential, if it exist, must be less than *00079 of the elec- 
tromotive force of a Daniell. The result of Sir William 
Thomson is therefore confirmed. 

There are many other points of interest in Clifton's paper, 
but, as the results are given in most instances as preliminary, 
we need not discuss the matter farther. 

Before leaving this subject, it may be well to notice that Sooroe of 
there is one point which is not touched by all these ex- ^^ei^ 
periments, viz., the question whether there is or is not a **""^' 
contact force between metals or even liquids and air. It 
has not yet been shown that the results of the experiments 
which are supposed to demonstrate that ZnjCu is about 
half the electromotive force of a Daniell could not be equally 
well explained by supposing the difference of potential to 
be* Cu| A -f A|Zn -f CujZn, whence CujZn is very small 
compared with Cu{A and A|Zn. This supposition would 
not invalidate Volta's law; nor would it contradict 
Clifton's results, for we have, in accordance with his experi- 
ments, on the new hypothesis, 

Aq.1 A + Cu| Aq + AqjCu = Aq| A -H Zn] Aq + AlZn, 

therefore, transposing, 

Zd| Aq + AqjCn -H Ca|A + A|Zu s , 

which, according to the new hypothesis, means that copper 
and zinc immersed in water are at the same potential In 
this view, the important part of the contact force usually 
observed between zinc and copper would be Cu|A + A|Zn,* 
which must therefore, by Sir Wm. Thomson's result, be the 
same as Cu|Aq + AqjZn. 

It is not very easy to see how this point is to be settled 
by direct measurements of electromotive force. Supposing, 
however, that it were settled, and that the contact force 
between two given metals A and B, and between each of 
them and a given liquid L, were known, then the differ- 
ence of potentials between the two metals when immersed 
in any liquid could be predicted iu all cases, and also the 
initial electromotive force tending to send a current through 
a circuit made by connecting the metals together and dip- 
ping them into the liquid. 

A number of cases of this kind have been investigated G«r- 
by Qerland ;^ but satisfactory agreement between theory Iw^d" 
and observation has been attained in but a few cases. "*^** 
Researches of this kind are beset with a double array of 
almost insuperable difSculties. 

The direction of the initial resultant electromotive force 
in any circuit of two metals and one fluid may be found by 
observing the first swing of a galvanometer through which 
the circuit is suddenly connected. Considerable precau- 
tions must be taken to obtain consistent results, and when 
all care has been taken, it is not found that the results of 
one observer always agree with those of another. This is 
scarcely to be wondered at, when we consider the dif&culty 
of making sure that in two diflerent experiments we are 
operating with absolutely the same metals and fluid in 
absolutely the same conditions as to surface. 

When the current tends to pass from one metal to an- 
other through the liquid in which they are immersed, the 
former metal is said to be positive to the latter. If the 
whole electromotive force in the circuit be the sum of all 
the contact forces at the various junctions, then it follows 
easily that we ought to be able to arrange the metals in a 
series, such that any one in the series is positive to any 
following one and negative to any preceding when both 
are dipped in the same liquid. It does not follow that the 
order of the series is the same for different liquids ; this 
would be so if the metallic contacts alone were operative. 

Many electromotive series of this kind have been given 
by difl'erent experimenters; but they have lost much of their 

> A sUnds for air. « See MazweU't EleUrioity, toL L | 249. 
' See Wiedemann, Bd. L $ Se. 



ELECTEICITY 



[ELKCTSOIfOnrX I 



Bleetro- interest now tbat tlie tbeorf of metallic contact, pure end 
J^**™ dmple, is given up. The following set is given by Fara- 

TwT ^ay-— ' 



S; 


^^:j' 


IICl. 


HNO, 

Csliorjg). 


KHO. 


Kna- 


KfS 


Ag 


Ag 


Sb 


Hi 


A? 


Pe 


Fe 






Ab 








Ni 


Sb 


Sb 




Cu 


Bi 


Bi 


Bi 


Hi 


Bi 


Cq 


Fo 


Pb 


Sb 


Ni 


Ni 




Bi 


Bi 




Pb 


Fa 


Fo 




Fe 


Pb 






Sn 


Pb 




Sd 


Sb 






Pb 


an 


Sn 


Pb 


Cd 


Ca 


Cd 


Cd 


CJ 


Ql 


Zo 


Sn 


Zn 


Cu 


Za 


Zd 


Zn 


CU 


Zn 


L-d 


Zn 



It will be seen that the order of the metals la not the tame 

for diSereat Hqnids. 

Qj^j^ Just as between different metala and between metals 

oTtwa ftnd liquids there is a contact force, so there is a contact 

llqnldt. force between different liquids. The dirtd, observations of 

this contact force are very few and uncertain. One thing, 

however, is settled, viz., that the contact forces between 

liquids do not universally at least obey the law of Volta, 

or, at all events, do not form a consistent series with the 

metals ; for a great variety of circuits of one metal and 

two solutions luve been discovered in which the resultant 

initial electromotive force is not zero. Faraday^ has even 

found cases of this kind with one metal and two different 

Btrengths of the mme solution. 

The cell of Becquerel is a favourite illustration of such a 

ctrcnit It consists of a porous vessel filled with a solution 

of potash and immersed in a beaker containing nitric acid ; 

two strips of platinum immersed in the potash and nitric 

acid respectively form the plates. The current goes in the 

cell from the potash to the nitric acid. The following 

ftdditional examples are taken from Wiedemann.^ 

One The current flows from the metal through the liquids in 

matd the order named to the same metal again. For brevity, 

"idhro ji,g metel is named only once. 



H«M1. 


u.n^^ 


MFInW. 


Pt 


KHO 


Acids 


Pt 


CuSO, 


DU. H^O. 










a, 


L 


Dil. HNO, 


H 


Cone.H^, 


HNO, 




KCy 


HNo', 



L ittnd* for Zn, Ca, or Pt. 

U „ Cn, Fe, Pb, 3u, or Ac. 

a „ Hi, Bi, PI, Hg, Pd, Sb, Fe, C, Ag, Zn, Co, Cd, or Sn. 

Two A. great variety of active voltaic circuits have been formed 

netAU with two liquids and two metals. The best known class of 

■od two cases is that in which the metals are in contact^ as in the 

"^nw*- two-fluid batteries of Daniell, Grove, and Bunaeg. But 

Faraday* gives a list of some thirty cases in which the 

fluids and metals are placed alternately, so that there is no 

metallic contact. He marks the following combinations as 

powerful : — 



Dilated nitric acid. 

Hydrochlori'i acid. 
Solatton of com. salt. 
Potasainm nil ph ids. 
Strong nitric acid. 



Qreen nitrooi acid. 



t be carefully noticed that the galvanometer indi- 




cation in the first instant only is to be considered. After 
the first rush of electricity the direction even of the cotrent 
may alter. Above all, no conclusion concerning the valne 
of the initial electromotive force is to be drawn from 
measurements of the subsequent current. Quantitative Ucti 
determinations of the electromotive force in many of the nuot 
above cases have been made by various methods, of which ~|^ 
an account will be found in Wiedemann's Galvaniitntu, ^^^ 
Bd. i. g 230. The most convenient plan is to use Thomson's 
quadrant electrometer, Lippmann's capillary electrometer, 
or some other instrument which allows us to measure the 
electromotive force while no current is passing through the 
cell. The galvanometer may also be used as in Latimer 
Clark's modification of FoggendorS's compensation method. 

The apparatus may be arranged according to the scheme Uetbi 
in fig. 53. ABC denotes part of the resistance in theofPoi 
circuit of the battery K ; the circuits ApELB, AjFMC ^ 
each contain a gal- 
vanometer, a cell, f-~- i li , diA. 
and a key. The 
cells E and F are so 
arranged as to tend 
to send currents in 
the same directions 
as K, but the re- 
sistances AB, AC 
are so adjusted that 
when the key L or 
the key M is de- f"W- 63- 
preased, no current is indicated by p or q. When this is 
80, we mustobviously have E-V*- V.,F-Vi- Vo, Ac, 
v., Vb, Vc denoting the potentiab at &, B, and (X 
Hence, if F, Q, R denote the resistances in AB, AC, and 
in the whole circuit of K, 

.b.|k, ,4k. 

It K were a constant battery, and its internal reeiatance 
were either known oc else so small as to form only on in- 
appreciable fraction of R, then each of the eqnaliona jost 
written might be naed singly, and we might operate with 
one cell and one galvanometer, comparing the electiomotive 
foree of the cell with E. In general, however, thia will 
not be possible, and then vre have, eliminating K and B, 
E P 
F°Q' 
from which wo get the ratio of E to F independent of tiie 
variation of K and R. We can by this method therefore 
find the ratio of the electromotive force of a given oom- 
bination to that of a standard cell, when no current is pass- 
ing through either. The process wonld be perfect in 
practice if a standard cell could be constructed whoM abso- 
lute constancy could be relied on. 

Contact foree from polariatlum. — The flow of ebrtii- 
city through the cell is accompanied by a deposition of the 
products of chemical decomposition on the plates, which 
altera the surface contact forces. Thb constitntes the 
phenomenon of polarization, which we have already par- 
tially studied. It will be useful to consider a little more 
in detail some of the forms in which it b met with. 

The products of electrolysis which accumulate at tboTirietl 
electrodes may be simply held in solution or precipitated,''!!''* 
or they may combine chemically with the solntiun; they 
may be deposited as a crost on the electrode, or they may 
enter into more or less intimate connection with it. Several 
of these different effects may occur together; bnt in almost 
all cases the result is the same, vix. a great weakening of 
the current after the first instant or ao. This W( 
of the current might be due either to a transition n 
caused by the alterations at the electrodes, or to an op 



SLIOrSOMOTIVB FOBOE.] 



ELECTRICITY 



87 



posing electromotive force arising from the alteration of 
the contacts. The former was the explanation adopted in 
the earlier researches of Poggendorff and Fechner; but 
there can be no doubt about the existence of the latter 
effect, and Lenz showed that it was sufficient to account 
for the facts observed. It has been usual, therefore, to 
•!• neglect the transition resistance altogether in the great 
i^ msyority of cases. It is certain, however, that it really exists 
^^^ in some instances. Clonsider the case of two electrolytic 
cells containing concentrated sulphuric acid, the electrodes 
being in the one copper plates, in the other platinum plates. 
Either of these ceUs inserted into a voltaic current will 
weaken the current, but for different reasons. In both 
cases hydrogen is freed at the negative electrode, and 
reduces sulphur from the strong acid, the effect of which 
is not great either way, for if the negative electrode be 
replaced by a fresh plate the weakening of the current 
remains. At the positive electrode oxygen is evolved, 
which oxidizes the copper in the one case and is deposited 
on the platinum in the other, — in both cases replacing the 
positive electrode by a fresh plate will cause momentary 
increase in the current ; but the copper plate which served 
as positive electrode if tested against a fresh copper plate 
gives very little return current, whereas the positive plati- 
num plate similarly tested gives a very powerful one. In 
the one cell the weakening of the current was due to the 
resistance of a crust of non-conducting copper oxide, in the 
other it was due to the contact force at the surface of the 
oxygenated platinum.^ 

The polarization which arises from the deposition of gas 
v^" on the electrodes is, if we except the case where peroxides 
are formed, by far the most powerful form, and has been 
much studied ever since voltaic batteries were used. Ex- 
periments like the one just quoted prove decisively that 
the dectromotive force has its seat at the surface of the 
electrode itself, and is due to local alterations there. The 
certainty of this fact gives the study of the phenomenon 
great theoretical importance, since we may hope thereby to 
arrive at some idea of the nature of the contact force. 

It is also certain that in most cases each electrode con- 
tributes separately to the whole electromotive force, for if 
we remove the polarized plates the adhering gas goes with 
them, and each plate is found to be electrically different 
when tested against a fresh or unpolarized plate. We 
may also take measures to remove the deposited gas by 
washing the plates with water, potash, or nitric acid, or by 
igniting them ; and it is found that the more energetic the 
chemical agency thus employed the more thoroughly is the 
polarization destroyed. 

It seems clear, therefore, that it is the mere fact of the 
presence of the gas on the electrode in some form or other 
which causes the electrical difference. We may go still 
further and produce the phenomenon by depositing gas by 
means other than electrolytic. If a piece of platinum foQ 
be immersed in hydrogen it absorbs the gas, as has been 
shown by Graham. A piece of foil thus treated is positive 
to a piece of freshly ignited foil when both are placed in 
dilute sulphuric acid. The same result is obtained by satu- 
rating the liquid in the neighbourhood of the foil with 
hydrogen.* The activity thus conferred on the plate may 
be again destroyed by immersing it in chlorine or bromine, 
or even in oxygen, by igniting it, and so on. Similarly, 
if we dip a fresh piece of foil into chlorine or bromine, it 
will become negative to a fresh plate. The effect obtained 
by dipping the foil in oxygen in the ordinary state is very 
small, the oxygen deposited by electrolysis must therefore 
be in a different state to that condensed during mere im- 



mersion in the gas. This is probably due to the fact that 
electrolytically generated oxygen contains ozone (see art 
Electbolysis ); and in accordance with this we find that 
a platinum foil ozonized by being held in the electric brush 
proceeding from a charged conductor, or rubbed with 
phosphorus, is negative to a fresh plate in dilute sulphuric 
acid. 

The gas battery of Grove is a remarkable instance of the electro- GroWt 
motiye properties of gas-coated metals. Two long glass tubes A gas 
and B are arranged in the two necks of a Woolfe's bottle. The batteiy.' 
upper ends of the tubes are closed, but pierced by two platinum 
wires, to which are fastened two long strips of platinum foil (which 
are sometimes platinized)' reaching to very near the lower ends of 
the tubes. The bottle and part of the tubes are filled with some 
liquid, say dilute sulphuric acid, and hydrogen introduced into B 
and oxygen into A. This may be very conveniently done by send- 
ing an electric current from A to B and decomposing the dilute 
acid, but it may be done in other ways as well. This arrangement 
has an electromotive force comparable with that of a DanieU's cell 
(see below, p. 88), and if the original volume of hydrogen in B be 
twice that of the oxygen in A it will continue to send the current 
through a closed circuit, the gas gradually disappearing in the tubes 
until none is left, when the current stops. These gas elements may 
be connected up in series, &c., and used like ordinary battery cells. 

If the tube 6 be filled with ordinary hydrogen and A with liquid 
only, a current in the same direction as before is observed ; but the 
liquid in A is decomposed and hydrogen evolved, which produces 
an opposing electromotive force and stops the current If A contain 
oxygen and B fluid only, the current lasts for a very short time 
unless the oxygen contain ozone. This is in accordance with what 
we have already seen. 

Grove ^ has given an electromotive aeries for the diiTerent 
and metals as follows: — 



Metals which do Alcohol. 

not decompose Sulphur. 

water. Phosphorus, 
Camphor. Carbonic oxide. 
Volatile oils. Hydrogen. 
Olcfiaut gas. Metals which de- 
Ether, compose water. 



conveo* 



* Wiedraumn, Bd. i. $ 456. 

* See Maoaloso's experiments, Wiedemann, A'aehMlife, S 58. 



Chlorine. 
Bromine. 
Iodine. 
Nitric oxide. 
Carbonic acid. 
Nitrogen. 

In this scries any member is positive to any preceding member. 

We have already remarked that the polarization in many Electro* 
cases comes on very rapidly. In cases where the electro- lytic 
motive force of the battery is not sufficient to produce a ^J' 
continuous evolution of gas, the current after the first rush 
dies away very rapidly. There are cases, however, in which 
a small current continues to flow for a very long time. 
Such currents are not accompanied by any visible evolution 
of gas, and it is clear that they could not be so accom- 
panied, for, if the electromotive force of the battery be 
under a certain limit, the amount of chemical energy 
absorbed by the current per unit of time is less than the 
intrinsic energy of the ions liberated in a unit of time. It 
was originally supposed, therefore, that, besides this 
electrol3rtic conduction proper, fluids conducted to a sli^t 
extent like metals. But Helmholtz ^ has shown that no 
such assumption is necessary, and has pointed out that 
when the fluid holds gas in solution a sort of electrolytic 
conduction may take place which involves, it is true, libera- 
tion of the ions, or at least of an ion, but so that the flnal 
result does not imply absorption of more energy than the 
battery can furnish per unit of time in accordance with 
Faraday's law of electrolytic conduction. 

Suppose, for instance, that the dilute sulphuric acid in an ordinary 
voltameter held II in solution. AVhon the current posses, appears 
at the anode and unites with the H in solution to form water ; a 
corresponding quantity of H is thereby liberated at the cathode, 
which is either absorbed by the platinum electrode or diffuses to- 
wards the ano«ie, to combine in its turn with the appearing oxygen. 
It is obvious that the liberation of the ion in such a case does not 
involve absorption of energj' to the extent necessarv when both H 
and are disengaged from' water. A current might therrfore be 
kept up under suoi circumstances for a long time by an electro- 

' This is best accomplished by washing the foils in hot nitric acid, 
and then using them to decompose a solution of platinic chloride with 
the current of two cells of Orov*. 

« PhiL Trans., 1845. » Pogg. Ann,, 1873. 



88 



ELECTRICITY 



[BLBOTBOMOnVB VOBCB. 



motive force under that of a cell of DanielL Helmholtz has given 
the name of electrolytic convection to this species of electrolytic 
conduction. He has shown that the phenomenon comes to an end 
when the liquid is perfectly freed from gas. The absorption of the 
gases by the electrodes plays a great part here, and gives rise in 
ffas-free liquids to a phenomenon analogous to the residual discharge. 
When the oattery is first turned on, a rush of electricity takes place, 
then there is a small current which gradually dies away. The first 
rush is like the instantaneous charge of a condenser; the small 
current which arises from the slow penetration of the ions into the 
platinum corresponds to the formation of latent charge. When 
the voltameter is disconnected from the battery and discharged 
through a galvanometer, we have a first rush due to the part of 
the ions accumulated on the surface of the platinum, and then a 
gradually decreasing current due to the emergence ot the gas which 
had penetrated into the metal. When the electromotive force which 
presses the gas into the electrode is removed, the absorbed gas will 
move very nearly in accordance with the ordinary law of diffusion, 
and the rate of its reappearance will depend very little^ on the 
electromotive force at the surface of the electrode. Consequently 
the residual current furnished by such an apparatus will not depend 
on its external resistance. A sudden increase of the external re- 
sistance will simply cause the current to diminish until sufficient 
surface density has been attained to raise the electromotive force to 
the value required to keep up the same current as before through 
the increased resistance; and the converse will happen if the 
external resistance be decreased. 

This passage of the gas into the substance of the electrode 
has, at the instance of HelmholtZy lately been investigated 
by Root.^ He finds that in certain cases, when only one side 
of a platinum foil is exposed to electrolysis, the deposited 
gas, whether H or O, actually passes through and produces 
the corresponding polarization on the other side of the foil. 
Maxi- It might at first sight be expected that in all cases where 

mum of the electromotive force in the circuit is sufficient to pro- 
polariza- ^[^53 continual evolution of the ions the polarization would 
^^ be the same. This is not by any means the case, however, 
owing to the fact that the final state of the liberated ions 
varies with the strength of the current, or, more correctly 
speaking, with the current density, i,e.y the amount of 
electricity which crosses unit section of the electrode in 
unit time. When Hg and O are being liberated from dilute 
H2SO4, this depends mainly on the formation of vari- 
able quantities of ozone and H2O2. This variation of 
the physical state and intrinsic energy of the liberated 
ions, is a fact of the greatest importance in the art of electro- 
metallurgy. A better instance could not be given than Qore's 
electrolytic modification of antimony, whose intiinsic energy 
is strikingly manifested by its explosive properties. 

The effect of enlarging the surface of the electrode in 
diminishing the polarization in the case where the maxi- 
mum polarization is not reached was noticed above (p. 48). 
It has also the eff'ect of diminishing the maximum of 
polarization in the case where the ions are completely set 
free. Platinizing has the same effect. Thus Poggendorff^ 
found for the maximum polarization 2 '12 to 2*32 ^ for 
bright platinum plates, while it was only 1 'SS to 1 '85 for 
platinized plates. The effect of platinizing on the hydrogen 
and oxygen polarization was about equal for strong 
currents, but greater on the hydrogen polarization when 
the current was weaker. On the other hand, by using 
small platinum points to decompose water in Wollaston's 
manner, Buff^ found the polarization as high as 3*31. 

Poggendorff^ and Crova*^ have investigated the depen- 
dence of the maximum of polarization on the current 
density. It follows from their researches that it can be 

represented by A - B"" , I being the current density. 

It would appear that the maximum of polarization is 
decreased by increasing the temperature of the celL The 

I — ^ — ■ 

* Within certain limits, of course. ' Pogg. Ann,, 1876. 

* Wiedemann, Bd. 1. § 480; Pogg, Ann.^ 1847. 

^ Unless otherwise stated, our unit of the electromotive force is for 
the present the electromotive force of a Daniell's ceU. 
» Wiedemann, Bd. L § 473 ; Pogg, Ann., 1867. 

* Pogg^ Ann., 1864. ^ Ann. de Chim, ei dc Phyt,, 1863. 



effect, however, in iome cases at least which have been 
adduced to prove this, might be explained by the decrease 
of the internal resistance of the cell 

Agitating the electrodes, stirring the liquid in their neigh- 
bourhood, or any other process which tends to dissipate 
the deposit on the electrode, leads, as might be expected, to 
a diminution of the polarization. The effect of increased 
pressure in retarding or helping electrolysis might be 
appreciable in certain cases. Suppose that an electro- 
chemical equivalent of the ions, during liberation under a 
pressure />, increases in volume by v, then during the pass- 
age of a unit of electricity work to the extent pv is done; 
the electromotive force required to free the ions must there- 
fore have a part equal to pu which may increase or de- 
crease as the process goes on. If the ions be gases which 
obey Boyle's law very nearly, then pv is constant, so long 
as the temperature remains the same ; so that we cannot 
expect, within reasonable limits, to check the electrolysis of 
dilute sulphuric acid by conducting it in a closed vessel® 

We have repeatedly drawn attention to the rapidity with Bapidit 
which the polarization decays in the first few instants after of <^ 
the plates are connected through a circuit of moderate resist- ?y"" 
ance. Direct proofs of this have been given by Beetz ^ and 
Edlund^^. The former shows that the oxygen polarization 
decays much more rapidly than the hydrogen polarization, 
which is not to be wondered at, considering the greater 
readiness of platinum to absorb hydrogen; with palladium 
electrodes the difference would doubtless be still more 
marked. The reader may also consult an interesting paper 
on this subject by Bernstein ^^ who concludes that in a 
certain case the polarization diminished by ^ to 1^ of its 
value in about ^^ of a second. 

There seems to be little reason to doubt the substantial 
accuracy of the facts just mentioned ; and the reader will 
not fail to see the application to the theory and practice of 
the measurement of the electromotive forces of inconstant 
electromotors, a category under which, unfortunately for 
the electrician, all known voltaic batteries must be classed. 
The remark applies with double force to the measurement 
of the electromotive force of polarization. Many measure- 
ments of the latter have been made. We quote a few, to 
give the reader a general idea of the magnitudes involved; 
into a discussion of the methods we cannot enter here. 

Hydrogen and Oxygen PolarizcUian of bright Platinum Platei.^* Nunwri 

calre- 
saltL 



Whole Polarization- 


n PoUrization. 


Polarization. 


Otwerver. 


2-33 
2-56 
2-31 
2-33 

• • • 


■ • • 

• • ■ 

115 
116 
115 


• • • 

• • • 

116 
116 

• • • 


Wheatstone^ 

Bnff. 

Svanberg. 

Poggcncbrff. 

Beetz. 



Polarization 0/ Platinum Places with different Oases compared with 
the Electroinotive Force of Platinum PlcUes with the same Oasei 
against afresh Platinum Plate in Grove's Oas Battery. ^^ 



Gas 


Polarization. 


PtaiPiL 


I 


•171 


•161 


Br 


•329 


•323 


CI 


•505 


•466 


H 


•910 


•814 


CI and H 


1'375 


1-^6 






1 



* Maxwell, vol. i. § 263. Other matters of great interest are stated 
there. See also the InstmctiTe analysis of the phenomena of polariza- 
tion in §§ 294-271. * Pogg- Ann., 1850. 

*• Pogg. Ann., 1852 ; see also Wiedemann, Bd. i. 9 495 ; Ice 

" Pogg. Ann., 1875. " From Wiedemann, Bd. L J 478. 

^' Beetz, quoted in Wiedemann ; Pogg, Ann^ 1853. 



■LIOTSOMOTITB fORCB.] 



ELECTRICITY 



89 



MarimUian of various Metals measured with Thomson^ s Quadrant 

EUetrcnuter^ 


Oz7gtn PUte. 


Hydrogen PUte. 


Poltrlxation. 


No. of CelU in 
Polftilzing BatUty. 


Fndily ignited Pt 

Pd 
Pt 
Fe 
Fe 
Al 


Pt 
Pd 
Pt 
Fe 
Pt 
Fe 
Al 


1-64-2-30 

l-60-r85 

1-60-1-91 

2-16 





1-09-5-20 


1-8 

1-4 

1-4 

3 

3 

3 

1-6 



risa- Although the polarization by gas deposits has absorbed 
in so much of the attention of physicists, it is by no means a 
'^ solitary instance. The phenomenon is universal It ap 
pears even With zinc plates in zinc sulphate, and copper 
plates in copper sulphate. The nearest approach to unpo- 
larizable electrodes is the case of amalgamated zinc plates 
in zinc sulphate, originally discovered by Du Bois Hey- 
mond. When the sulphate solution is neutral, the polari- 
zation, as may be shown by immersing a large number of 
plates in series in the sohition, is extremely small. 

For an account of polarization at the surface of two 
liquids observed by Du Bois Reymond, and other kindred 
matters, and for many other facts which we have passed 
over in silence, the reader may consult Wiedemann's Gal- 
fxtniamus. Some account will be found in the article 
Electroltsis of the remarkable phenomenon of the 
'' |)assivity of iron, and of the powerful polarization arising 
from the formation of superoxides, on which depends the 
action of the secondary pile of Plante.'' 

Application of the Laws of Energy to the Voltaic Circuit, 
— In the classi^ series of researches by which Joule laid 
the foundations of the laws of energy, a considerable share 
of attention is devoted to the energetics of the electric 
current Quided by the great idea which he was gradually 
developing, Joule made experimental determinations of the 
amount of energy of various kinds evolved in the electric 
circuit We have already seen how he measured the 
quantity of heat developed in a metallic conductor, and in 
an electrolyte.^ This quantity was found to vary as the 
product of the resistance of the conductor into the square 
of the current strength, account being taken of disturbances 
at the electrodes in the case of electrolytes. 

These disturbances were considered in the first memoir 
and allowed for. The accuracy of the view taken of them, 
to which Joule was led by the opinion of Faraday, that 
the solution of the oxide in the voltaic cell had no active 
share in producing the electric current, was justly ques- 
tioned, implicitly by Sir Wra. Thomson' in 1851, and ex- 
plicitly by Bosscha* in 1859. 
'g In a later memoir, however,* Joule made a direct experi- 
«. mental investigation of these secondary effects, and shows 
how they can be accounted for. His results have not been 
shaken by subsequent investigators ; and the general con- 
clusions to be drawn from them arc not in the least 
affected by the theory of secondary action, which is sug- 
gested in the paper. These, so far as we are now con- 
cerned with them, are as follows : — 

" Ist In an electrolytic cell there are three distinct 
obstacles to the voltaic current The first is resistance to 
conduction ; the second is resistance to electrolysis vnihout 
chemical change' [arising simply from the presence of 

^ Tait, Phil, Maff., 1869. This method is in some respects one of 
the best for measurements of the kind. 

• Pha, Mag., 1841. » PhU. Mag,, 1851 (2). p. 654. 

• Pogg, Ann., cviii. p. 819. 

* Mem, LiL and PhiL Soe. Manchester, 2d ser. vii., 1843. 

* This resistance is, in more modem language, an ** opposing elec- 
tromotive force." 

f The maanixig of " withoat chemical change** will be teen directly. 



chemical repulsion] ;^ and the third is resistance to dectrth 
lysis, accompanied by chemical changes. 

** 2d. By the first of these (the resistance to conduction) 
heat is evolved exactly as it is by a wire, according to the 
resistance and the square of the current ; and it is thus 
that a part of the heat belonging to the chemical actions 
of the battery is evolved. By the second a reaction on the 
intensity^ of the battery occurs, and wherever it exists heat 
is evolved exactly equivalent to the loss of heating power 
in the battery arising from its diminished intensity. But 
the third resistance differs from the second, inasmuch as 
the heat due to its reaction is rendered latent, and thus 
lost to the circuit 

'' 3d. Hence it is that, however we ai range the voltaic 
apparatus, and whatever cells of electrolysis we include in 
the circuit, the whole caloric of the circuit is exacUy 
accounted for by the whole of the chemical changes. 

** 4th. As was discovered by Faraday, the quantity of 
current electricity^^ depends upon the number of atoms 
which suffer electrolysis in each cell; and the intensity 
depends on the sum of chemical affinities. Now both the 
mechanical and heating powers of a current are (per equiva- 
lent of electrolysis in any one of the battery cells) propor- 
tional to its intensity. Therefore the mechanical and 
heating powers of the current are proportional to each 
other. 

'' 5th. The magnetic electrical machine enables us to con- 
vert mechanical power into heat by means of the electric 
currents which are induced by it ; and I have little doubt 
that, by interposing an electromagnetic engine in the circuit 
of a battery, a diminution of the heat evolved per equiva- 
lent of chemical change would be the consequence, and 
this in proportion to the mechanical powers obtained."^^ 

The above statement of Joule's contains, in a form which 
seems to us neither ambiguous nor obscure,^^ an exposition 
of the leading experimental principles of the energetics 
of the electric circuit Besides the papers of Joule we 
have mentioned, two others on the electrical origin of the 
heat of chemical combination ought to be read in connection 
with this subject ^^ The now famous tract of Helmholtz, 
" Ueber die Erhaltung der Kraft," which appeared in 1847, 
shortly after these papers of Joule, did much, by its able 
statement of the issues, to advance this branch of electrical 
science, and should be consulted by every thorough student 

An extremely important contribution to the experimental FaTPs*i 
evidence for the law of energy in the case of electric cur- "^_,^ 
rents was furnished by the researches of Favre.^* He uses 
a calorimeter, which is virtually a mercury thermometer 
with an enormous bulb, into which are inserted a number 
of test-tube shaped vessels all opening outwards. When a 
heated body is placed in one of these vessels its heat is 
quickly communicated to the mercury in the calorimeter, 
and the amount of heat thus communicated is measured 
by the expansion of the mercury, which is measured as 
usual by noting the displacement along a capillary tube. 
Into one of the recesses of the bulb of this calorimeter 
containing a quantity of dilute sulphuric acid was intro- 
duced 33 grm. of granulated zinc. The heat evolved 
during its dissolution was 18682 units (gramme-degrees C). 
Five of the recesses were then furnished with dilute sul- 
phuric acid of the same strength as before, and into them 
were put five elements of Smee (amalgamated zinc and 



* The brackets here are ours ; they contain Joule's theoretical view 
with which we are not now concemecL 

• Tn modem phrase, " electromotire force.' 



*» 



*® That is, current strength. 

" This he experimenUUy verified, Phil, Mag., 1848. 

" Cf. Venlet, Th^orie Micanique de la Chaleur, § 827. 

" PhU. Mag., 1842 (1). and 1843 (1). 

i« Am. de Chim, tt de Phys,, 1854. 

VIIL — 13 



90 



ELECTRICITY 



[electkomotitb romcE, 



Theory 
of Sir 
Wm. 
Thorn- 
fon. 



Thom- 
son's 
law. 



platinized copper). These were joined up in circuit by 
means of very thick copper wire, and the heat developed 
during the solution of 33 grm. of zinc observed as before. 
The result was 18674 units, ue,, almost exactly the same 
as before. A small electromagnetic engine was next in- 
troduced into the circuit, and the heat observed, first, 
when it was at rest; secondly, when it was in motion, but 
consuming all its energy in heat owing to friction, <bc. ; and 
thirdly, when it was doing work in raising a weight. The 
quantities of heat in the three cases were 18667, 18657, 
and 1 837 4 units respectively. In the first four experiments, 
therefore, the heat developed in the circuit is sensibly the 
same, the mean being 18670; the heat developed in the last 
case is less than this by 296, which is the equivalent of the 
potential energy conferred on the raised weight. From this 
result the value of the mechanical equivalent of heat ought 
to be 443. This differs considerably from the best value 
(423 to 425), but not more so than might be expected from 
experimental errors. 

Dynamical Theory of the Mectromotive Force of the 
Battery. — In two very important papers published in the 
Philosophical Magazine for 1851, Sir William Thomson 
laid the foundations of the Dynamical Theory of Electro- 
IjTsis, one of the objects of which, to use very nearly his 
own words, is to investigate, for any circuit, the relation 
between the electromotive force, the electrochemical equi- 
valents of the substances operated on, and the dynamical 
equivalent of the chemical effect produced in the consump- 
tion of a given amount of the materials, and by means of 
this relation to determine in absolute measure from experi- 
mental data the electromotive force of a single cell of 
Daniell's battery, and the electromotive force required for 
the electrolysis of water. 

The relation sought for is found as follows. Let E be 
the electromotive force ^ of the battery. Then, by the 
definition of electromotive force, E is the whole work done 
in the circuit by a unit current during a unit of time. 
This work may appear as heat developed in the conductors 
or at the junctions according to the laws of Joule and 
Peltier, as the intrinsic energy of liberated or deposited 
ions, as work done by electromagnetic forces, as " local 
heat'' in the battery (see below, p. 91), or otherwise. Let 
e be the electrochemical equivalent of any one of the 
elements which take part in the chemical action from 
which the energy of the current is derived, i.e., the num- 
ber of grammes of that element which enter into the 
chemical action during the passage of unit current for a 
second; and let be the thermal equivalent of that amount 
of chemical action in the battery into which exactly a 
gramme of the element in question would enter, — in other 
words, the amount of heat that would be developed were 
the whole energy of the amount of chemical action just 
indicated spent in heat. Then it is obvious that the 
energy of the chemical action that takes place in the 
battery during the passage of unit current for a unit of 
time is JeO, where J is Joule's equivalent. Hence, by 
the principle of conservation, we must have 

E = Je^; 
or, in words, the electromotive force of any electrochemical 
apparatus is, in absolute measure, eqtial to the dynamical 
equivalent of the chemical action thcU takes place during the 
passage of unit current for a unit of time. 

The value of J is known, being 4156 x 1(H in absolute 
units. The value of e has been found by various experi- 
menters (see below, p. 104), the most accurate result being 
probably that deduced from the experiments of Kohl- 
rausch, viz. <?= -003411 for zinc. 



^ All our quantities arc measured, of coarse, in C. G. S. absolute 
units. 



We may find by direct calorimetric experiments on Galea] 
the heat developed in the circuit. In this way Joule tionfh 
found for the thermal equivalent of the chemical action of ***?* ^ 
a Daniell's cell during the solution of 65 grammes of zinc^J^ 
47670 (grm. deg. C), and Eaoult^, by a somewhat similar drcuit 
process, obtained the number 47800. These give for the 
heat equivalent of the chemical action during the solu- 
tion of 1 grm. zinc 733 and 735 respectively. Substitut^ 
ing these values in our formula, we get for the electro- 
motive force of Daniell's cell in absolute C. G. S. uniti 
1039x108 or 1-042x101 

But we may proceed in a totally different way to find Cueoii 
the value of $. Direct observations have been made ontionfri 
the heat evolved in a great variety of chemical actions, <^^*«"^ 
and from these experiments we can calculate with a con- ^^ 
siderable degree of accuracy, the value of 0, and thus 
deduce the electromotive force of a battery from purely 
chemical data. This method of procedure must of course 
be adopted if we wish to test the dynamical theory. Now, 
neglecting refinements concerning the state in which the 
copper is deposited, the state of concentration of the solu- 
tion, (S:c., the chemical action in a Daniell's cell may be 
stated to be the removal of the Cu from CuSO^ in solu- 
tion, and the substitution of Zn in its place. Now, Favre 
and Silberman have found for the heat developed in this 
chemical action 714 (grm. deg. C.) per grm. of zme. 
This will give, by the above formula, for the electromotive 
force of Daniell's element 1*012x10®. The chemical 
action might also be stated as the combination of zinc 
with oxygen, and the solution of the zinc oxide thus 
formed in sulphuric acid, the separation of copper oxide 
from sulphuric acid, and of the copper from the oxygen. 
The quantity of heat evolved in the first two actions per 
grm of zinc is, according to Andrews, 1301 -f 369 = 1670 
(grm. deg. C), and that absorbed in the last two actions 
588 -h 293 = 881. Hence ^ = 789; this gives MlSxlO®. 
Professor G. C. Foster^ has calculated from Julius Thom- 
sen's experiments values 805, 1387, and 617 of 6 for the 
cells of Daniell, Grove, and Smee respectively; the values 
of the electromotive forces corresponding to these are 
1-141x10^ 1-966x10; and -875 x 10«. These results 
are in fair agreement with the different values of the 
electromotive force obtained from direct experiment 

It follows from Thomson's theory that a certain mini- limit o 
mum electromotive force is necessary to decompose water; elMtro* 
and he calculated from the data of Joule that this mini- "*^" 
mum was 1 318 times the electromotive force of a Daniell's ^^ 
cell. Favre and Silberman found for the heat developed lydi 
in the formation of RJd 68920, from which we conclude 
that the minimum electromotive force required to electro- 
lyse water is 68920-^47800, *.<?., 1*44 times that of a 
Daniell's cell* 

Development of Heat at the Electrodes, — In a remarkable Local 
paper,^ which we have already quoted, Joule investigated hot 
directly the disturbing effect of the electrodes on the heat 

« Wiedemann, Bd. ii. 2, § 1118. 

3 Everett, lUustrations of C, 0, S, System of Units, p. 77. Ne 
reference to the source is given. 

* Verdet {Thiorie Mic. de la Chdleur, torn. ii. p. 207) states that 
Favre was the first to point this out, but gives no citation. It Memt 
unlikely that Favre considered the matter so early as 185L (Sas 
Violle's bibliography at the end of Verdet's volume. ) 

» Mem. Lit. and Phil. Soc. Manchester, ser. 2, vol. viL, 1848. 
This paper seems to have been in a great measoro lost sight of. In 
his earlier papers {Poffff. Ann., ciii. §504, 1858) Bosscha says he 
had not seen it. Poggendorfif, in a note, p. 504, appreciates it in 
a manner which appears to us unjust This may have arisen fh)in 
misunderstanding of Joule's terminology, however. Venlet {ChaUmr, 
tom. ii. p. 204) does not seem to have been acquainted with it. It 
IS mentioned in the bibliography by M. J. Violle, however, andtr 
1846, which is the date of the volume of the Memoirs in whidi il 
was published. The paper was actually read Jan. 1 843. 



XUKTBOMOTiyB FOSOE.] 



ELECTRICITY 



91 



•*• developed in an electrolyte. His method was as follows. 

'^ A ooil of wire whose resistance was known in terms of a 
certain standard was inserted in the circuit of six Darnell's 
elements, and the heat evolved in it carefully measured by 
immersing it in a calorimeter. The resistance of the rest of 
the circuit, including that of the battery, was found by 
interpolating a known resistance in the circuit and observ- 
ing, by means of a tangent galvanometer, the ratio in 
which the current was reduced. (The assumption is here 
made that the electromotive force of a Daniell's cell is 
constant for different currenta) Knowing the heat evolved 
in a part of the circuit of known resistance, and knowing 
the resistance of the whole circuit, the heat evolved accord- 
ing to Joule's law in the whole circuit during the oxida- 
tion of 65 grammes of zinc can be calculated from the 
indications of the tangent galvanometer previously com- 
pared with a voltameter. Hence the thermal equivalent 
% of the work done by the electromotive force of a 
Daniell's cell during the solution of 65 grm. zinc can be 
found. The value of arrived at by Joule in this way is 
47670 (grm. deg. C). 

Electrolytic cells of various construction were then in- 
serted into the circuit The electromotive force resisting 
the passage ef the current through the cells was found by 
taking the number of battery cells just sufficient to pro- 
dace electrolysis, observing the current, then increasing the 
number of cells by one and observing the current again. 
If t be the current in the first case, corrected to bring it 
to the value it would have had if the resistance of the 
whole circuit had been the same as in the second case, and 
J the current in the second case, then, E being the 
nnmber of battery cells used in the first case, the electro- 
motive force Z opposing the current is given by 

the unit being the electromotive force of a Daniell's cell. 
Z being known and assumed constant for different currents 
within certain limits, the resistance of the whole circuit, 
electrolyte included, can be found by Ohm's method as 
above. The amount of heat H which ought to be de- 
veloped in the electrolyte by Joule's law can then be 
calculated. The amount of heat H' actually developed 
was observed. It was found that H' is in general greater 
than H, the difference per electrolysis of 65 grm. zinc with 
various electrodes is shown in the following table : — 



Eleetroda. 


z 


H'-H 


L 


Z-L 


+ 


- 


Pt 
Pt 

Pt» 
Pt» 


Amg. Zn 
Pt 

p9 

Pt^ 


2-81 
2-47 
1-75 
1-90 
1*90 


66300 
53000 
16400 
28800 
26700 


1-89 

111 

•34 

•60 

•56 


1-42 
1-36 
1-40 
1-29 
1*34 



^ Platinized. 

The electrolyte in all these cases was dil. HJSO^, excepting 
(he last case, where it was a solution of potash of sp. g. 
1*063. In all the cases the chemical process is finally the 
aame or very nearly so, viz., the freeing of the elements of 
water, hydrogen and oxygen, in the ordinary gaseous^ 
state, and the transference of a certain quantity of H2SO4 
from the negative to the positive electrode, or of alkali in 
the opposite direction. Yet the values of H'-H (which 
we may call the local heat) are very different. It will be 
seen, however, that the values of H' - H and Z rise and fall 
together; and, if we calculate the electromotive forces (L) 
eorre^Kmding to the values of H' - H, by dividing by 47670, 
which was found for the thermal equivalent of the electro- 

> TIm ammmt of oxxgen that finally etcapes in the active etate as 
08006 ia vary noall. 



motive force of a Daniell's cell, and subtract the values of 
L thus found from Z, we get results which are not far 
from constant The mean of the values of Z - L is 1*36, 
the thermal equivalent of which is 64800, which is not 
very different from 68900, the heat evolved in the com- 
bination of 2 grm. of H with 16 grm. of O to form water. 
It appears, therefore, that the local heat corresponds to the 
excess of the electromotive force of polarization over the 
electromotive force requisite to separate water into its 
component gases. In other words, the work done by the 
current against this residual electromotive force is accounted 
for by the local heat H'-H developed in the cell (see 
Joule's statement above, p. 89). A glance at the column L in 
the above table shows that this residual electromotive force 
depends greatly on the nature of the electrodes. Thus 
when the positive and negative electrodes are plates of 
platinum and zinc respectively the residual electromotive 
force is 1*39, whereas with platinized silver plates it is 
only '34. Local heat and the corresponding electromotive 
force play a very important part in the working of batteries. 
Owing to this cause there is an evolution of heat in the cell 
itself which varies with the strength of the current, and 
uses up a certain definite fraction of the energy furnished 
by the solution of the zinc. By sufficiently increasing the 
external resistance, the amount of heat developed in the 
cell according to the law JH » HI^ can be made as small 
a fraction as we please of the whole heat thus developed ; 
but the amount of local heat generated in the cell during 
the solution of 65 grm. zinc is not greatly altered in this 
way, at least not in a cell of Daniell, or in any other of 
the so-called constant batteries. Did our space permit we 
might quote a great variety of experimental results to 
illustrate the principles we have been discussing. Most 
of these investigations are due to the French physicists 
Favre and Silbermann, whose researches have greatly ad- 
vanced this department of the science of energy. 

Very copious extracts from the memoirs of these and 
other physicists who have worked in this department will be 
found in Wiedemann, Bd. ii. 2, §§ 1121 sqq. The reader 
who desires to follow this interesting subject to the sources 
will find his labour much lightened by referring to M. J. 
Viollc's excellent bibliography of the mechanical theory 
of heat, appended to the second volume of Verdet's Theorie 
Mecanique de la Chaleur, Much has been done for the 
theory of the subject by a series of papers on the 
mechanical theory of electrolysis by Bosscha,^ in which the 
somewhat complicated phenomena involved are analjrsed 
in a remarkably clear and able way. Any reader who 
desires to know what has been done in this department 
will do well to consult these papers. We quote the fol- 
lowing as an example of Favre and Silbermann 's results 
and of the calculations of Bosscha. 

The heat evolved in a cell of Smee' and in platinum 
wires of different lengths through which it was circuited 
was measured with the following result : — 



Local 
heat and 
reddaal 
electro- 
motive 
forocu 



Favre 

and 

Silver 

manD. 

Boncha. 



Heat in cell. 


Heat in wire. 


Length of wire. 


Heat in cell cak. 


18127 

11690 

10439 

8992 


4965 
6557 
7746 
9030 


25 mm. 

50 „ 
100 „ 
200 „ 


13528 

11788 

10188 

9048 



The heat in each case is that evolved during the libera- 
tion of 1 grm. of hydrogen in the celL If we assume that 
the whole heat in the cell and in the wire is generatdl 
according to Joule's law, and calculate on this hypothesis 
the resistance of the cell in mm. of the wire, we should get 



' Poffg. Ann., ci., ciii., cv., cviii., 1867, Ice. 
' Amalgamated zinc aad platinized copper. 



92 



ELECTRICITY 



[xUOTBOHOTm woacE, 



YBlutm varying from 66 to 200 ram. If, however, we 
aasume, in accordance with the principles explained above, 
that a conBtant fraction of the whole energy per grm. 
of liberated hydrogen appears as local heat in the cell, 
then, Q denoting the whole heat which appeals in the cell, 
L the local heat, H the heat in the wire, E the resistance 
of the cell, S that of the wire, we have 
Q-L_R 
H S '• 
and it is found that on making R°32'3 and L-=r589, 
this formula will represent the resulta of experiment very 
fairly. The last column in the above table gives the value 
of Q thus calculated. In geneial ho good an agreement 
is not to be expected, because L may and does vary with 
the strength of the current. 
ThtoriM Thus far we have been dealing with the direct results 
ofrad- of experimeat, but when we inquire into the reason for 
dacko- '''^ exietenco of this residual electromotive force and of the 
motiT*" l***^' development of heat corresponding to it, and, in 
(ait«. particular, when we aslc why the effect is so much greater 
with some metals than with others, the answers become less 
tatisfactoiy. We meet, in fact, with considerable divergence 
of opinion. 

Joule's view was that the effect is due to the affinity of 
the metal of the electrode for oxygen. Thb is endorsed 
to a certain extent by Sir William Thomson, who puts the 
matter thus:* — "In a pair consisting of zinc and tin the 
electromotive force has been found by Poggendorff to be 
only about half that of a pair consisting of zinc and copper, 
and consequently less than half that of a single cell of 
Smee's. There is therefore an immense loss of mechanical 
effect in the external working of a battery composed of such 
elements, which must be compensated by heat produced 
within the cells. I believe, with Joule, that this compensa- 
ting heat is produced at the surface of the tin in con- 
sequence of hydrogen being forced to bubble up from it, 
instead of the metal itself bemg allowed to combine with 
the oxygen of the water in contact with it. A most curious 
result of the theory of chemical resistance is that, in ex- 
perimenta(such as those of Faraday, £xp. Ree., 1027, 1028) 
in which an electric current passing through a trough con- 
taining sulphuric acid is made to traverse a diaphragm of 
an osidizable metal (zinc or tin) dissolving it on one side 
and evolving bubbles of hydrogen on the other, part (if 
not all) of the heat of combination wi)l be evolved, not ou 
the side on which the metal is being eaten away, but on 
the side at which the bubbles of hydrogen appear. It will 
be interesting to verify this conclusion by comparing the 
quantities of heat evolved in two equal and similar electro- 
lytic cells in the same circuit, each with zinc for negative 
dectrode, and one with zinc the other with platinum 'or 
platinized silver for the positive electrode."' 

Bosscha dissents from the theory of "chemical resistance" 
thus expounded, and advances a different explanation. 
According to him, the local heat arises from the energy 
tost by the liberated ions in passing from the active to the 
ordinary state. We know that the hydrogen which is 
being liberated at the surface of an electrode can effect 
reductions which hydrogen in the ordinary state cannot 
accomplish; it is liberated in fact in a state of greater in- 
trinsic energy than nsuaL It is this excess of intrinsic 
energy which appears as local heat, and gives rise to the 
residual electromotive force in electrolysis. Different 
metala possess in very different degrees the power of re- 
dncingactive hydrogen to the ordinary state; and therefore 

> PkO. Mag., 1851 (21, p. 666. 

* The effect here predicted «u afterwutli abserred by Thomion 
blmselt Rip. BriL Auoc, 1&62, and later itill bj Bouchs, Pegg. 
Amtn ciiL p. G17 



the proportion of hydrogen which gets away from the 
electrode in the active state differs according to cirenm- 
stances. Bosscha'a theory is that it is the intrinsic energy 
thus carried away from the electrode that appears as local 
heat Similar remarks apply of course to oxygen, the 
active form of the gas being probably ozone. As a veri£ca- 
tion of the theory, the fact is cited that at the surface of a 
plate of carbon, which possesses in an eminent degree the 
power of Inducing ozone to the ordinary state, the residual 
electromotive force and local heat are very smalL At all 
events the theory of " chemical resistance " is held to be 
inadequate to explain the facta; for calculating from some 
results of his own, combined with those of Len£ and 
Saweljew, he finds for the residual electromotive force at 
electrodes of 

Pt Fe Cu Sn Hg Zn 

■i& -it -64 -as 1-21) 1-20; 

from which it appears that the order of magnitude of the 

electromotive forces is not that of theoffinitiesof the metals 

for oxygen. 

Eleclricai ifeatur* of Chemical Affinity. — In a paper' sent to U^. 
tbe French Academy to compete for s prize offered for the beat esniy mre. 
on the heat of chemical combination, Joule elabontea an inKenioni mant a 
methodformeaaurins chemical affinity. By direct obserrstion it ii chnsiB 
ascertained how much heat is developed in a given time in a certain alfiiih, 
standard coil of irire, when it is traversed by a cnnnt whoae Jouii. 
strength is measured by means of a tangent galvanometer. Then 
three reodinga of the tangent finlvanometer are taken — first, when 
the galvanometer alone is in circuit with the battery, secondly, 
when the standard coil is also inaerteij, thirdly, when an electio- 
lytic cell is inaerteii instead of the coil. The amount of the iona 
liberated and the heat evolved in the cell during a given time ia 
also observed in the last case. If A, B, C be the re^inga of the 
galvanometer in the three cases, and if x be the rtsitlanee of a 
melallic tcire capable of retarding tht eurmd equally mUt the 
eleclTobjtic all* then we easily get, taking the redstanc* of tha 
standard coil as unity, 

(A- cm 



Now if the resistance x were put in the place of the electrolytic 
cell, the current would be the same ; hence by Faraday's law the 
amount of chemical energy absorbed in the battery would be tbe 
same. Also the heat evolved iu the rest of tbe circuit, excluding z, 
would be the aame. It follows, tlierefore, that the heat H wkiA 
vxuld he evolved in i is the equivalent of the whole energy riven 
out in the electrolytic cell. If therefore we lubtract from H the 
heat K which actually anpears in the cell, the Tcmainder H - E ia 
the heat cnuivalent of the intrinsic energy of the liberated iout; 
and, provided they appear finally in the "ordinanr"* Condition, 
H~E is the heat which would be developed when they ara allowed 
to combine. 

In this way Joule found for the heat evolved in tha comlnutioB 
of 1 gnu. of copper, liuc, and hydrogen respectively S&4, 11S5, 
33SS3. 

Gaivanie Batteries. — It would be inconsistent with onr 
general plan to attempt an exhanstive discussion of all the 
different electromotors which depend for their energy on 
chemical action. Wiedemann's Galvaaitmue, or books on 
telegraphy and other arts in which electricity is applied to 
technical purposes, may be consulted by the reader who 
wishes for fuller information. A brief discussion of some 
typical batteries will, however, be useful, were it only to 
illustrate the principles we have just been laying down. 

All the earlier batteries were one-fluid t»tterieiL The 

> Noticed in the OrnipfM Afxiftu, Feb. 1846, and published at laogtb 
la Phil. Mag., 1852, 

* Notice that it is not said that x is equal to tbs reditanee of the 
electrolyte. Boucha in tha papers we have quoted, either ftmn not 
having seen the paper we are now analysing, or through a misnndar- 
itaDding, accosei Joule of error here. Tbe reasoning (Pogg. ,.4Hik, d. 
p. 640) which he seems to quote from Joule is not to be foond in thi« 
or in an; other of Joule's papers that we know of. FolariialioD i* 
taken into account by Joule (see PUI, 3lag.,lZS2{l), p. 486). Tb« 
eiitidsTDS of Verdet, who seems to follow Boaecha, an equally groiuill- 
laa irhiorie Mieanupie de la Omieur. i. ii. p. 204). 

* nils word ia left purponcly a little vague, and Is oaed to avoia a 
longdl " '^- 



XLBontoHonvs force.] 



ELECTRICITY 



93 



did plates usually conaisted of zinc and copper, and the 

I*** exciting fluid was in general sulphuric acid. Various 
improvements were made by Cruickshank, WoUaston, Hare, 
and others, in the way of rendering the battery more com- 
pact, and of reducing its internal resistance by enlarging 
the plates. Hare carried the last-mentioned improvement 
to great lengths ; by winding up together in a spiral form 
sheets of copper and zinc, insulated from each other by 
pieces of wood, plates of 40 or more square feet surface 
were obtained. In this way the internal resistance was 
veiy much reduced, and powerful heating effects could be 
obtained. When small internal resistance is no object, the 
cells of the battery may be filled with sand or sawdust, 
moistened with the dilute acid. In this form the battery 
is more portable. 

There are two capital defects to which all one-fluid batteries 
are more or less subject. In the first place, whether there 

^ b or is not external metallic connection between the plates, 
a certain amount of chemical action goes on at the surface 
of the zinc, which consumes the metal without aiding in 
the production of the current. To this is given the name 
of local action. It is supposed to arise from inequalities 
in the zinc, on account of which one portion of the metal 
is electropositive to a neighbouring portion; hence local 
currents arise causing an evolution of hydrogen at some 
places and solution of the zinc at others. In the second 
place, when the battery is in action, there is always 
an evolution of hydrogen at the copper or electro- 
negative plate of the cell, a certain amount of which 
adheres to the plate and causes a strong electromotive 
force of polarization. The first of these evils is re- 
medied to a great extent by amalgamating the zinc 
plate. We thus reduce the surface metal to a fluid condi- 
tion everywhere, and thereby eliminate differences of hard- 
ness and softness, crystalline structure, and so on. The 
oldest method was to use zinc amalgam for the electro- 
negative metal ; but it is now universally the custom to 
amalgamate the surface of the zinc plates simply, which 
may be done by rubbing them with mercury under dilute 
sulphuric acid. No such effective cure has been found for 
the hydrogen polarization. Smee introduced the plan of 
using instead of the copper plates thin leaves of platinum 
or silver foil, which are platinized by the process already 
described (p. 87). This, in accordance with what we have 
already seen, diminishes the polarization.^ A similar 
result is obtained by using for the electronegative plate 
cast iron or graphite; the action of the latter is much 
improved by steeping it in nitric acid. 

This last fact introduces us to a new principle for im- 
proving the action of batteries, viz., the use of an oxidizing 

' agent to get rid of the hydrogen polarization. When the 
plates of a Smee's battery have been exposed to the air for 
some time, it is always found that the current is much 
more energetic than usual just after the first immersion. 
The improvement is of course only temporary, for the stock 
of oxygen is soon exhausted, and on raising the plates and 
dipping them again immediately , the phenomenon does 
not appear. Davy found that dilute nitric acid acted 
better than dilute sulphuric acid as an exciting fluid, and 
the cause of this is the action of the HNO3 ^^ *^® hydro- 
gen evolved at the copper plate. Good instances of this 
kind of action are furnished by the bichromate battery of 
Bunsen and the L^clanchd cell, which occupy a sort of 
middle position between one and two fluid batteries. 

The bichromate cell consists of an amalgamated zinc plate, nra- 
ally rospended between two parallel carbon plates, so that it can be 
railed or depressed at pleasure. The bichromate solution is made, 

* Fleeming Jenkin gives *47 volt as the available electromotive 
force of Smee*s ceU. The electromotive force when the drcoit is 
broken is mack greater. See above, p. 90. 



batteries. 



according to Hansen, by mixing 605 parts of water with 61*8 of 
potassium bichromate and 116 of sulphuric acid. The electro- 
motive force of the bichromate cell is very mat to start with (more 
than twice that of a Danieirs cell), but it falls very quickly when the 
external resistance is small. The cell recovers pretty quickly how- 
ever, and may be used with advantage where powerful currents of 
short duration are often wanted. In the cell of L^lanch^ the 
electronegative metal is replaced by a porous vessel filled with 
carbon and pjounded peroxide of manganese. The exciting liquid 
used is chloride of ammonium. Chloride of zinc is formed at the 
zinc plate, and ammonia and hydrogen appear at the negative 
plate ; the latter reduces the MnO„ so that H,0 and Mn,0, are 
formed, while the ammonia is parti v dissolved and partly escapes. 
This element is tolerably constant if it be not used to produce very 
strong currents, but its great merit consists in being very permanent; 
for it will keep in condition for months with very little attention, 
furnishing a current now and then when wanted ; hence its exten- 
sive use in working electric bells, railway signals, and so on. 

It cannot be said that any of the batteries we have Two- 
described, or in fact any battery on the one-fluid S3r8tem, ^^^ 
satisfies to any great extent the requirements of a constant 
electromotor, which are to give the same electromotive 
force whatever the external resistance, and to preserve that 
electromotive force unaltered for a considerable time. The 
best solution of the problem to construct a constant battery 
is the two-fluid principle invented by Daniell ; and on the 
whole, the best application of that principle is the cell 
originally given by him. This consists essentially of a 
plate of copper immersed in a saturated solution of copper 
sulphate, and a plate of zinc immersed in dilute sulphuric 
acid or zinc sulphate, the copper solution being sepa- 
rated from the other by some kind of diaphragm, usually 
a porous vessel of unglazed earthenware. The chemical 
action consists of the solution of the zinc plate to form 
zinc sulphate, the formation of zinc sulphate at the dia- 
phragm, and the deposition of copper at the copper plate ; 
thus : — 

Zn S04Zn SO^ 1 80^ SO^^Cu Cu 

gives Zn^^ ZnSO^ Zn | SO4 CUSO4 5uCu . 

The evolution of hydrogen and the polarization arising 
therefrom are thus avoided. 

A very common arrangement of this cell is a porous vessel, con- Da- 
taining the copper plate and the sulphate of copper, with a small niell*! 
store of largo crystals to keep the solution saturated. This vessel element, 
is dipped into another nearly filled with a semi-saturated solution 
of zinc sulphate, in which is placed the zinc plate. With a UtUe 
care to keep the cell clean by occasionally removing some of Uie 
zinc solution and diluting to prevent incrustation, to feed the 
copper solution, so that it may not eet weak and deposit hydrogen 
instead of copper on the copper plate, to keep down the level of 
the copper solution, which is constantly rising by osmose (see 
art Electrolysis), and a few other obvious precautions, a bat- 
tery of Danieirs cells will furnish a very nearly constant cur- 
rent, and keep in order for a long time. It is necessary to keep the 
current going, otherwise the solutions diffuse through the porous 
vessel, the result of which is a deposit of copper on the zinc, and 
other mischiefs, which stop the action of the cell altogether. 

Daniell*s element has been constructed in a great variety of 
forms, to suit various purposes. The sawdust Daniell, invented 
by Sir Wm. Thomson* (1858), is very convenient when portability 
is desired. In this form the copper plate, soldered to a gutta- 
percha covered wire, is placed at the bottom of a glass veeael and 
covered with crystals oi copper sulphate ; over these wet sawdust 
is sprinkled, and then more sawdust, moistened with a solution of 
sulphate of rinc, upon which is laid the zinc plate. The cell of 
Minotto is very similar to this. 

In these batteries the sawdust takes the place of the porous 
diapbniCTi, and retards the interdiffusion of the fluids. In another 
class of batteries, of which the element of Meidinger may be taken 
as the type, the diaphragm is dispensed with altogether, and the 
action of gravity alone retards the diffusion. In Meidinger's cell 
the zinc is formed into a ring, which fits the upper part of a glaas 
beaker filled with rinc sulphate. At the bottom of this beaker is 
placed a smaller beaker, in which stands a ring of copper, with a 
properly insulated connecting wire. The mouth of the beaker is 
closed by a lid, with a hole in the centre, through which passes 
the long tapering neck of a glass balloon, whi(^ is filled with 

• Jenkin, Electricity and Magjietism, p. 224. 



94 



ELECTRICITY 



[ELBCTROMOnYX WOBCM, 



czyitalB of copper sulphate ; the narro-w end of this neck dips into 
the small beaker, the copper sulphate runs slowly out, and being 
specifically heavier than the zinc sulphate, it collects at the 
bottom about the coppet ring. 

Yet another form of Daniell's element is the tray cell of Sir 
William Thomson, which consists of a large wooden tray lined with 
lead, the bottom of which is covered with copper by clectrotyping. 
The zinc is made like a grating, to allow the gas to escape, 
and is enveloped in a piece of parchment paper bent into a tray- 
ahape, the whole resting on Uttle pieces of wood placed on the 
leaaen bottom of the outer tray. Sulphate of copper is fed in at 
the edge of the tray, and sulphate of zinc is poured into the 
parchment. The zincs in these elements are some 40 centi- 
metres square, so that the internal resistance is as low as '2 ohm. 
Grove's One of the best known in this country, and perhaps the most 
element, used of all the two-fluid cells, is the element of Grove. This 
differs from Daniell's element in having nitric acid with a plati* 
num electrode in the porous cell, instead of the copper solution and 
the copper electrode of Daniell's element. The hydrogen evolved 
at the platinum is oxidized by the nitric acid, and the polarization 
thus avoided. The nitrous fumes given ofi" by the chemical 
action are very disagreeable, and also very poisonous, so that it is 
advisable to place the battery outside the experimenting room or 
in a suitable araught chamber. The electromotive force of Grove's 
cell is a good deiQ higher than that of Daniell's, and its internal 
resistance is very mucn less, -25 ohm being easily attained with a 
cell of moderate dimensions. On this account the cell is much 
used for working induction coils, generating the electric light, and 
so on, notwithstanding that it is troublesome to fit up, and must 
be renewed every day. 
Cells of '^ Bunsen's element the platinum foils of Grove are replaced by 
Bunsen carbon. The prime cost of the battery is thus considerably re- 
Ijg^ ' duced, the more so now that carbons for the purpose have become 
articles of commerce. The electromotive force of the element thus 
altered is as great as, or with good carbons even greater than, in 
Grove's original form ; but the internal resistance is greater. There 
is a difficmtv sometimes in obtaining good connection with the 
carbons, and trouble arises from their H)uling ; but the fact that 
this cell is a universal favourite in Germany proves its practical 
utility. It is comparatively little used in this country. 

In the cell of Mari^ Davy, which is, or was, much used for tele- 
graphic purposes in France, the copper solution and copper plate of 
Daniell are replaced by a watery paste of protosulphate of.mercurj% 
into which is inserted a carbon electrode. The electromotive force 
of this cell is said to bo about 1 -5 volts, ^ and its internal resistance 
to be greater than that of DanielPs cell. 

Besides these, various bichromate elements of merit might be 

described ; but we have dwelt long enough on this subject already. 

The following table of Latimer Clark's, quoted by Maxwell, will 

give the reader an idea of the relations as to electromotive force of 

the commoner elements : — 



Daniell 

Do. 

Do. 
Bunsen 

Do. 
Grove 


H,S04+ 4Aq 
H^04 + 12Aq 
H,S04 + 12Aq 
H,S04 + 12Aq 
H,S04 + 12Aq 
H^S04+ 4Aq 


CuSO^ 

CuSO. 

Cu(NO,), 

HNO, 

HNO,(8p.g.l-88) 

HNO, 


1-079 
0-978 
1-000 
1-964 
1-888 
l-95« 



See- 
beck's 
dis- 
covery. 



The electromotive force is stated in volts, and the solutions in 
the third column are concentrated, unless it is otherwise stated. 

Thermodectriciiy, — We have already alluded to the law of 
Volta, according to which there can be no resultant electro- 
motive force in a circuit composed solely of dififerent metals ; 
and it will be remembered that we added the condition 
that all the junctions must be at the same temperature. 
Seebeck was the first to discover ^ that this law is subject 
to exception when the junctions are not all at the same 
temperature. If we form a circuit with an iron wire and 
a copper wire, and raise the temperature of one of the 
junctions a little above that of the other, a current flows 
round the circuit, passing from copper to iron over the hotter 
junction ; similarly, if we solder together a piece of bismuth 
and a piece of antimony, and connect the free ends with the 
copper wires of a galvanometer, then when the junction of 
the bismuth and antimony is heated the galvanometer 
indicates a current passing from bismuth to antimony over 
the hot junction. It will be perceived that the second of 

1 Jenkin, EUctricily and MagneHam, p. 225. 
' Pogg, iinn., vi. 1826. The discovery was made about 1821 or 
1822. 



our two illustrative instances is more complicated than the 
first, inasjnuch as three metals enter into the circuit in- 
stead of two. Nevertheless the experimental result is not 
altered by the intervention of the copper wire (abstraction 
being made of its resistance), provided the temperatures of 
the points where it joins the bismuth and antimony re- 
spectively be the same. It is easy to give a direct experi- 
mental proof of this assertion by inserting between the 
pieces of bismuth and antimony a piece of copper wire so 
that the circuit now is Bi.Cu.Sb.Cu.BL ; if the junctions of 
the inserted wire with the bismuth and antimony be raised 
to the same temperature as the BiSb junction in our second 
experiment, and the junctions with the copper wire of the 
galvanometer be at the same lower temperature as before^ 
the total electromotive force in the circuit will be the same ; 
and, provided the resistance of the circuit has not been 
sensibly increased by the interpolation of the copper wire, 
the galvanometer indication will also be the same as before 
The same result is obtained however many different metals 
we insert between the bismuth and antimony, provided the 
temperatures of all the junctions be the same and equal to 
that of the BiSb junction in the original experiment 

The law of Volta therefore still holds if stated thos : 

A series of metals whose junctions are all at the same 

temperature mxiy he replaced by the tioo end m^eUs of the 

series without altering the electromotive force in any circuU 

of which the series forms a part. 

It is not unlikely that the above statement of the fundamental 
facts concerning thermoelectromotive force has suggested to tiie 
reader two notions : — 1st, that the phenomena may be completely 
explained by a coTiUut force at the junctions of the metals which is a 
function of the temperature of the junction; and 2d, that this con- 
tact force is the true contact force of Volta. It is perhaps as well 
to mention even at this early stage that the first of these notions 
is certainly not correct, and that the second is not admitted by acyme 
of the greatest authorities on the subject. 

Seebeck examined the thermoelectric properties of a laige Thenix 
number of metals, and formed a thermoelectric series, any «l«cWe 
metal in which is thermoelectrically related to any following "***'' 
one as bismuth (see above) is to antimony, the electro- 
motive force in a circuit formed of the metals being ceteris 
paribus greater the farther -apart they are in the series 
The following is a selection from Seebeck's series : — 

Bi.Ni.Co.Pd.Pt.Cu.Mn.Hg.Pb.Sn.Au.Ag.Zn. 
Cd.Fe.Sb.Te. 

This series has only a general interest, and is not to be re 
garded as in any way absoluta Seebeck himself showed the 
great effect that slight impurities and variations of physical 
condition may have on the position of a metal in the series. 
Some specimens of platinum for instance come between 
zinc and cadmium. Another instance of the same kind is 
afforded by iron : Joule ' found the foUowing order to 
hold — cast iron, copper, steel, smithy iron. 

Thermoelectric series have been given by Hankel, 
Thomson, and others, but we need not reproduce them here. 
It may be well, however, to direct the attention of the 
reader to the properties of metallic sulphides and of alloys 
which in many cases occupy extreme positions in the 
thermoelectric series. Alloys present anomalies in their 
thermoelectric properties somewhat similar to those already 
noticed in our discussion of their conductivity. These 
properties have been much studied with a view to practical 
applications in the construction of thermopiles. Consider- 
able progress has been made in this direction (see above 
p. 11), notwithstanding the fact that many of the alloys 
most distinguished for their thermoelectric power are veiy 
brittle and have a tendency to instability under the con- 
tinued action of heat* 

» PhiL Mag., 1867. 

* For further information consult Wiedemann, (Tdfo., Bd. L 
% 593. &c. 



ILEOTBOMOTIYB fOSCB.] 



ELECTRICITY 



95 



Many measurements of the electromotive force of thermo- 
^ electric couples have been made by Matthieasen,^ Wiede- 
^^ Biaon,^ K Becquerel,^ and others, but the results are of no 
great value owing to the effect of impurities and the want 
of sufficient data to determine all the thermoelectric con- 
stants of any one couple (see below, p. 99). Numerical 
data, such as they are, will be found in Wiedemann, 
Fleeming Jenkin's EUdridty and Magnetism^ or Everett's 
JlluUrcUions of the CerUrefnetre-gramme^econd Si/stem of 
Units. It will give the reader an idea of the order of the 
magnitudes involved to state that the electromotive force 
at ordinary temperatures of a BiSb couple is somewhere 
about 11700 C. G. S.^ absolute units when the difference 
between the temperatures of the junctions is 1" C. The 
corresponding number for a CuFe couple is 1600 or 1700. 
Thermoelectric currents, or at least what may very likely 
be such, have been obtained in circuits other than purely 
metallic, e. g.j in circuits containing junctions of metals and 
fluids,^ metals and melted salts,^ fluids and fluids.^ Tlie 
phenomena in all these cases are complicated, and the 
results more or less doubtful ; so that no useful purpose 
could be served by discussing the matter here. The same 
remark applies to the curious electrical phenomena of 
flames,^ of which no proper explanation, so far as we know, 
has as yet been given. 
y^. The experiments of Magnus ^ have shown that in a 
itf of circuit composed entirely of one metal, every part of which 
S>nu- is in the same state as to hardness and* strain, no thermo- 
electromotive force can exist, no matter what the varia- 
tions of the section or form of the conductor or what the 
distribution of temperature in it may be (so long as there 
is neither discontinuity of form nor abrupt variation of 
temperature). 

This statement is of great importance, as we shall see, 
in the theory of thermoelectricity. Its purport will be all 
the better understood if we dwell for a little on the three 
limitations which accompany it 

The great effect of the hardness or softness and crystalline 
or amorphous structure of a metal on its electric properties 
was observed by Seebeck soon after the discovery of thermo- 
electricity.^® The effect of temper in wires may be shown 
very neatly by the following experiment due to Magnus. 
On a reel formed by crossing two pieces of wood are wound 
several turns of hard-drawn brass wire softened in a 
number of places aciyacent to each other on the reel The 
free ends of the wire being connected with a galvanometer, 
and the parts of the wire lying between neighbouring hard 
and soft portions being heated, a thermoelectric current 
of considerable strengUi is obtained, whose direction is 
from soft parts to hard across the heated boundaries. 
Effects of a similar kind were obtained with silver, steel, 
cadmium, copper, gold, and platinum. In German silver, 
«nc, tin, and iron, the current went from hard to soft 
across the hotter boundary. 
^^ Sir William Thomson made a number of experiments on 
tnin, the effect of strain on the electric propertieo of metals. 
The results, some of them very surprising, are contained 
Wm. in his Bakerian Lecture,^i along with many other things of 
great importance for the student of thermoelectricity. 
Two of his experiments may be described as specimens. 



« Oalv., Bd. I. § 590. 



* Poffg. Ann., 1858. 
*Ann,de Chim, el cU Phys,, 1864. 

* That la, roughly, -000117, if we take for our unit the electro- 
motiTo force of a Daniell's cell. 

• By Walker, Faraday, Henrici, Gore, and others; see Wiedemann, 
«u i. § 639, kc. 

tjl-^^^"^^ ^^*^ ^^'* ^^^^J Hankel, Wiedemann (L «.), Gore, 
PniL Mag., 1864. 

' Nobili, Wiedemann, Becquerel; see Wiedemann, I c 

• See Wiedemann, I e. » Pogg. Ann,, 1851. 
" Pogff. Aim^ 186d. u phiL Trans,, 1856. 



They afford convenient lecture-room illustrations of the 
subject under discussion. (1.) A series of copper wires 
A, B, C, D, E, F, Q, <fec., are suspended from a horizontal 
peg. A and B, C and D, E and F, &c., are connected by 
short horizontal pieces of copper wire, all lying in the same 
horizontal line, and B and C, D and E, F and Q, d^c, are 
connected by a series of pieces lying in another horizontal 
line below the former. An arrangement is made by means 
of which the alternate wires A, C, E, O, can be more or less 
powerfully stretched, while B, D, F, <kc., are comparatively 
free. A piece of hot glass is applied to heat either the 
upper or lower line of junctions. A thermoelectric cur- 
rent is then observed passing from the stretched to the 
unstretched copper across the hot junctions. This thermo- 
electric current increases with the traction up to the break- 
ing point But the most remarkable point that comes 
out in such experiments is that when we free the wire 
after powerful traction, leaving it with a permanent set, 
there is still a thermoelectric current ; but the direction is 
now from the soft or unstrained towards the permanently 
strained parts across the hot region. (2.) Iron gives 
similar results, only the direction of the current is in each 
case opposite to that in the corresponding case for copper. 
The following experiment exhibits this in a very elegant 
manner. One end of a piece of carefully annealed iron 
wire is wound several times round a horizontal peg, the 
free end being slightly stretched by a small weight, and 
connected with one terminal of a galvanometer. The 
other end of the wire is wound a few times round one 
side of a rectangular wooden frame, the free end being 
stretched by a small weight and connected with the other 
terminal of the galvanometer. The parts of the wire on 
the peg or the part on the frame is then heated, and 
weights are hung to the frame. As the weight increases, 
the deflection of the galvanometer goes on increasing. If 
we stop a little short of rupture, and gradually decrease 
the weight, the deflection of the galvanometer gradually 
decreases to zero, changes sign before the weight is entirely 
removed, and finally remains at a considerable negative 
value when the wire is again free. 

These experiments of Sir Wm. Thomson's were repeated Le Rooz, 
by Le Roux. The results of the two experimenters are ^^ 
not very concordant. This may be due to differences 
in the qualities of the materials with which they worked, 
or to the fact that Le Roux^^ worked at higher mean tem- 
peratures than Thomson. ^^ 

Le Boux also repeated the experiments of Magnus, Abrupt 
confirming his general result, but adding the two last ▼aria- 
qualifications given above. He found, contrary to the ^^ °^ 
result of Magnus, that when a lateral notch is filed in a ti^^**'*^ 
wire and one side heated, there is in general a thermo- 
electric current, which is greater, up to a certain limit, the 
deeper the notcL He also found that when two wires 
of the same metal, with flat ends, are pressed together, so 
that one forms the continuation of the other, and the wire 
on one side of the junction is heated, no current is ob- 
tained ; but he observed a current in all cases where there 
was dissymmetry, — e.g,, where an edge of one end was 
pressed on the flat surface of the other, where the wires 
overlapped or crossed, or where the chisel-shaped end of 
one wire fitted into a notch in the end of the other, and 
the axes of the wires were inclined, and so on. 

Whether a very abrupt variation in temperature in a 
continuous part of a metallic wire would produce a tbermo- 
electromotive force is a question which possesses little 
physical interest, since it is impossible to realize the 

^ Ann. de Ckxm. et de Phys., 1867. 

^* Wiedemann, Bd. L § 610. It appoan from a note at the end of 
Le Roax's paper (/.c.) that Sir Wm. Thomson han lately repeated 
some of his experiments and confirmed his former results. 



96 



ELECTRICITY 



imagiaed conditions. There can be no doubt, however, 
that, when the two unequally heated ends of a wire com- 
poaed of the same metal throughout are brought together, 
a thermoelectric current is in general the consequence. 
Such currents were, it appears, observed by Ritter^ in 
1801, when cold and hot pieces of zinc wire were brought 
into contact. Becquerel, Matteucci, Magnus, and others 
have eiperimented on this subject. The results obtained 
are, no doubt, greatly influenced by the state as to ozida' 
tion, &c., of the surfaces of the metals experimented on, 
as has been pointed out by Franz and Oaugain.. The 
experimental conditions are, in truth, very complicated, 
and a discussion of the matter would be out of place 
here." We may mention, however, that, at the instance of 
Professor Tait, Mr Durham* made experiments on the 
transient current which arises when the unequally heated 
ends oE a platinum wire are brought into contact. It was 
found that the first swing of a gdvanometer of moderately 
long period was proportional to the temperature difference 
and independent of the mean temperature through a con- 
siderable range. 
Tbarmo- Cumming, who ezpertmeDted on thermoelectricity about 
taw?" ^^^ """^ ^'""^ " Seebeck, and apparently independently, 
^,^ discovered the remarkable fact that the thermoelectric 
Com- order of the metals is not the same for high temperatures 
mlnK. as for low. He found that, when the temperature of the 
hot junction in a circuit of iron and copper, or iron and 
gold, is gradually raised, the electromotive force increases 
more and more slowly, reaches a maximum at a certain 
temperature T, then decreases to zero, and finally changes 
its direction, The higher the temperature of Uie colder 
junction, so long as it is less than T, the sooner the 
raveTsal of the electromotive force is obtained. If the 
temperature of the hot junction be t+r, where t is small, 
then the reversal of the electromotive force takes place 
when the temperature of the colder junction is T -r. If 
both junctions, A and B, be at ibe temperature T, then 
eithef heating or cotding A will cause a current ia the same 
direction round the circuit, and either heating or cooling B 
will cause a current in the opposite direction. 

The reversal of the current may be shown very conve- 
niently in the manner recommended by Sir Wm. Thomson.* 
A cirenit is formed by soldering an iron wire to the 
copper terminal wires of a galvanometer. If one junction 
be at the temperature of the room and the other at 300° C. 
or thereby, a current flows from copper to iron across the 
hotter junction ; but, if we rabe the temperature of both 
junctions overSOO'C, one being still a httle hotter than the 
other (which can be managed by keeping both in a lamp 
flame, one in a slightly hotter place than the other), then 
the current will flow from iron to copper across the hot 
junction. If both junctions be allowed to cool, the difftr- 
ence between their temperatures remaining the same, the 
current will decrease, becoming zero when the mean temps- 
lature of the two junctions is about 280° C. ; and, on still 
further lowering the mean temperature, it wiU set again in 
the opposite direction, i.e., from copper to iron across the 
hot junction. The fundamental fac^ of thermoelectric in- 
version were confirmed by Becquerel,* Hankel,' Svanberg,^ 
&e. ; but the matter rested there till it was taken up^ by 
Sir Wro. Thomson* in the course of his classical researches 
on the appLcations of the laws of thermodynamics to phy- 
sical problems. 

' Wiedemann, Bd. i. J 627. 

' Comnlt Wiedemmn, Bd. L | 627, *o., md Uucut, t. ii. § 832, fcc, 

'Pnc. R.a.E., 1B71-2. 

« BtkerUn Lertun, Phil. Trait*., 18SS, p. fl». 

' Jtm. dt Chim. tt de Fhya., 1826. » Fogg. Ann., lUL 

' Fogg. Ann., 1SS3 ; e/. Wiedemuin, Bd. i. J 623, 

■ ,_ ^ jj .pp,,^ f^ arammk of Joule'i, if.Prtie. 



The application of the firat law of thermodynamics leads to Apfib 
no difficulty; and it indicates that the heat absorbed acand- ^ "^ 
ing to Peltier's law, in the ordinary case when a conent f^^ 
passes from copper to iron across the hotter of the jtinctions, djM- 
minus the heat evolved at the colder junction where the mio. 
current passes from iron to copper, is to be looked on as a !?*- 
source of i)8rt at least of the ener^ of the thermoelectric ^^ 
current. If absorption or evolution of heat occur any- 
where else than at the junctions, this must be taken 
account of in a similar manner. 

The application of the second law is of a more hypo- 
thetical character. It is true that the Peltier effects, as 
we may for shortness call the heat absorption and evolatiou 
at the junctions, are reversible in this sense that we might 
suppose the thermoelectric current, whose enei^ arises 
wholly or partly from the excess of the heat absorbed at 
the junction A over that evolved at the junction B, used 
to drive an electromagnetic engine and raise a weight ; and 
that we might suppose the potential energy thus obtained 
again expended in sending, by means of tm electromagnetic 
machine, a current in the opposite direction ronnd the 
circuit, absorbing heat at B, evolving heat at A, and thus 
restoring the inequality of temperature. This process, 
however, must always be accompanied by dissip^ion of 
energy, (I) by the evolution of heat in the circuit accord- 
ing to Joule's law, and (2) by conduction from the hotter 
towards the colder parts of the wires. The first of these 
effects varies as the square of the current strength, while 
Peltier's effect varies as the current strength simply ; an 
that the former might be made as small a fraction of the 
latter as we please by sufficiently reducing the current, and 
thus, theoretically speaking, eliminated. The second form 
of dissipation could not be thus got rid of, and could only 
be eliminated in a cirenit of infinitely email thermal but 
finite electric conductivity, a kind of cireuit not to be 
realized, as we know {see above p. SI). Still it seems a 
reasonable hypothesis to assume that the Peltier effect^ 
and other heat effects if any, which vary as the first power 
of the strength of the current, taken by themselvei are 
subject to the second law of thermodynamics. Let us now 
further assume that aU the reversible beat effects occur 
solely at the juDctions. Let II, II' denote the heat 
(measured in dynamical equivalents) absorbed and evolved, 
at the hot and cold junctions respectively in a unit of time 
by a unit current. Let £ be the electromotive force of an 
electromotor maintaining a current I, in such a dir«cti(ai 
as to cause absorption of heat at the hot junction. Tlteii, 
if B be the whole resistance of the circuit, we have, bj 
Joule's law and the first law of thermodynamica, 

EI-^^I-^'I-BI' (l), 

supposing the whole of the energy of the current Tasted 
in heat Hence we get 



(2X 



JIS.E., 1874-6. p. «7. 



■ IVoiu. R.S.E., 18B1. 



It appears then that, owing to the excess of Hie absorption 
of heat at the hot junction over the evolution at the cold 
iunction, there arises an electromotive force U - II' helping 
to drive the current in the direction giving heat absorptioa 
at the hot junction. We may suppose (and shall hence- 
forth suppose) that £ = 0, and then the cnrrent will be 
maintained entirely by the thermoelectromotive force. 
If we now apply the second law, we get 

e e" ' 
and ff being the absolute temperatures of th« hot and 
cold junctions. Hence 



:, in Other words, 11 < 



• Ce, where Oil 



BUBOTBOHOnVS FOBGOl] 



ELECTRICITY 



97 



t 



i 



mz. 



ing only on the nature of the metals. In accordance with 
tluiBy the thermoelectromotive force in the circuit would be 
C(^ - ^); that is, it would be proportional to the difference 
between the temperatures of the junctions. Now this 
conclusion is wholly inconsistent with the existence of 
thermoelectric inversions. We must therefore either deny 
the applicability of the second law, or else seek for rever- 
sible heat effects other than those of Peltier. This line of 
reasoning, taken in connection with another somewhat 
more difficult, satisfied Sir Wm. Thomson that reversible 
heating effects do exist in the circuit elsewhere than at the 
junctions. These can only exist where the current passes 
from hotter to colder parts of the same wire or the reverse. 
Thomson was thus led to one of the most astonishing of all 
his brilliant discoveries; for he found, after a series of 
researches distinguished alike for patience and experi- 
mental skill, that an electric current absorbs heat in a 
copper conductor when it passes from cold to hot, and 
evolves heat in iron under similar circumstances. This 
phenomenon was called by its discoverer the electric con- 
vection of heat. He expressed the facts above stated by 
saying that positive electricity carries heat with it in an 
nnequally heated copper conductor, and negative electricity 
carries heat with it in an unequally heated iron conductor. 
The first statement is perhaps clearer ; the value of the one 
given by Thomson consists in the suggestion which it con- 
veys of a valuable physical analogy with the transport of 
heat by a current of water in an unequally heated pipe.^ 

If two points AB of a uniform linear conductor, in 
which a current I is flowing from A to B, and evolving 
heat, be kept at the same constant temperature, but for 
the electric transport of heat the temperature distribution 
would be symmetrical about a point of maximum tem- 
perature half way between A and B. Owing to the electric 
transport of heat, the maximum will be shifted towards A 
in iron, towards B in copper.^ This remark contains the 
principle of the experiments made by Thomson to detect 
the new effect. 

The first experiment in which the effect was satisfactorily estab- 
lished was made with a conductor ABCDEFO, formed of a num- 
ber of strips of iron bound together at A, C, £, and G, but opened out 
widely at B, D, and F, to allow these pails to be thoroughly heated 
or cooled. At C and £ small cylindrical openin|^ &owed the 
bulbs of two delicate mercurial thermometers to be inserted in the 
heart of the bundle of strips. The part D of the conductor was 
kept at 100* C. by means of boilinff water, and theparts B and F were 
kept cool by a constant stream of cold water. The current from a 
few cells of huge surface was sent for a certain time from A to 0, 
then for the same length of time from to A, and so on. In this 
way the effects of want of symmetry were eliminated, and the result 
was that the excess of the temperature at £ over that at G was 
always greatest when the current passed from G to A ; whence it 
follows, as stated above, that a current of positive electricity evolves 
heat in an iron conductor when it passes from cold to hot. 

Le Roux ' has made a series of iuterestinff experiments on the 
Thomson effect in different metals. He found that the effect varies 
as the strength of the current, and ^ves the following numbers 
representing its relative magnitudes in different metals. In lead 
the effect is insensible. 



+ 


- 


Sb 


64 


Fe 


81 


Cd 


81 


Bi 


81 


Zn 


11 


Aig 


25 


Ag 


6 


Pt 


18 


Cu 


2 


Al 


1 






Sn 


01 



We may now apply the mathematical reasoning given 
above, taking into account Thomson's effect 



* Trans, RS.E^ 1851. 

s See Verdet, TMorie MScanigve de la Chaleur, t. IL §250. 

* Anm. ds CMm. a ds Phys*, 1867 



Suppose for simplicity we have a circuit of two metals only. Let Eqoa- 
the current go from A to B over the hot junction, and let the heat tions of 
absorbed in passing from a point at temperature 9 to a neighbour- Thorn- 
ing point at temperature $+d$ in A bte aide per unit of current son. 
per unit of time ; let tr^B be the correspondinig expression for B. 
Then it is obvious, from the result of Magnus (see above, p. 95), 
that Cj and tr^ can be functions of the temperature merely ; they 
depend, of course, on the nature of the metal, but are independent 
of the form or magnitude of the section of the conductor. The first 
and second laws now give respectively 



E=n-n'+ 



/e' (*^i"*^«) 



de 



n n' re g-i-o-j 



" « e' y ^ e 



^de 



(4). 



(5), 



where £ is the whole thermoelectromotive force, and n and If are 
the same functions of e and ^ respectively. By differentiation we 
get from (5) 

Ujy-^'=' • • • • <«)•' 

whence we easily get 



or 




(7). 



This last equation enables us to determine £ in terms of n, and 
conversely. 

When the difference between the temperatures of the 
junctions is very small, equal to d$ say, the thermoelectra 
motive force is 



> 



(8). 



n 



The coefficient -^ by which we must multiply the small 

temperature difference to get the electromotive force is 
called by Thomson the thermoelectric power of the circuit 
If we have a circuit of three metals, A, B, C, all at the 
same temperature ^, then we know that 

nBo+ncA+nAB-»o, 

whence Hab Hag IIbo 

e " ~ * 



W; 



or, in other words, the thermoelectric power of B with 
respect to A is equal to the difference between the thermo- 
electric powers of a third metal C with respect to A and 
B respectively. 

Thus far we have been following Thomson. But as yet Tait*8 
we have no indication how o-, the coefficient of the Thomson cox^Jeo- 
effect, depends on the temperature. Thomson himself *'"*• 
seems (see his Bakerian Lecture, /. c, p. 706) to have ex- 
pected that o- would turn out to be constant Certain 
considerations conccmiog the dissipation of energy led 
Tait, however, to conjecture that o- is proportional to 
the absolute temperature. If we adopt this conjecture, 
Thomson's equations give us at once the values of the 
Peltier effect and the electromotive force in the circuit. 
If o-j = ki$y o-j = k^, we get from (6) and (7) successively* 






(10), 

(11), 



where ^^j is the neutral temperatura Also, since in a 
circuit of uniform temperature there are no Thomson 
effects, and the sum of the Peltier effects is zero, we get for 
any three metals 

(*t-^s)«is+(*8-*i)«si + (^-*t)«ii-0. . (12). 

Taking up the idea of a thermoelectric diagram origi- Thermo- 
nally suggested by Thomson, Tait has shown how to repre- electric 
sent the above results in a very elegant and simple manner, diagram 
Suppose we construct a curve whose abscissa is the abso- ?J^v!J*^ 
lute temperature $, and whose ordinate is the thermo-Taitf 
electric power of some standard metal with respect to the 

* Tait, Proc. R.&B., 1870-1-2. 

vin. — 13 



98 



ELBCTKICITY 



[cucTSOHOTtva roxtm. 



metal we ore considering, then, from what has been Bhown I thermoelectric diagram is a biokea line Diade up of two if 
(10), Tftit'e conjecture leads to the result that this curve is not three straight pieces. This peculiarity of the irtHt Una 
s straight line; and if the standard metal be lead, for was very strikingly shown hy forming circuits of iron with 
which, according to Le Roux's results, the Thomson effect ' the alloys Ftir or PtCu. Such ctrcnits exhibit tieo or nm 
is sero, then the coefficient k of the Thomson effect is the ' fAred Tteutral points {see fig. Bfi). Another very elegant 
tangent of the inclination of the repreaentatire line to the 
axis of abacisss. And not only so, but it follows from 
fonnnba (9) and (7) that, if A' AN, B'BN (fig 54) be the 



-f 












\ 










^^ 








\ 


Kl 






V 


\b 




^ 


\ 




.^:^— 


— 




'" \ 



Fig. 51. 
lines corresponding to two metals, say Cu and Fe (of which 
the former is abore the latter in the thermoelectric series 
at ordinary temperatures), and if AB, A'B' be the ordii^tes 
corresponding to fl and $\ then the electromotive force in a 
circuit of the two metals whose junctions are at the tempera- 
tures B and &, tending to send a current from Cu to Fe across 
the hotter junction, is represented by the area ABB' A', 
The Peltier effects at the two junctions are represented by 
the rectangles AB5a and A'B'6'a', and the Thomson effects, 
in the Cu and Fe respectively, by AA'DC and BB'CF, or 
by AA'o'o and BB'6'6, which are equal to these. At N, 
where the lines intersect, the Peltier effect vanishes. N 
therefore is the neutral point ; and, if the higher tempera- 
ture lie beyond it, the electromotive force must be found 
by taking the difference of the: areas NA'B' and NAB, and 
BO on. All the phenomena of inversion may be studied by 
means of this diagmm, and the reader will find it by far 
the best means for fixing the facts in his memory. 
Eipeii- For several years back Tait' and his pnpils havo 
JjMoti of been engaged in veri^dng the consequences of this con- 
■rtit, fto. jectnre ; and it has been shown, first, for temperatures 
within the range of mercury thermometers, and latterly 
tor temperatures conaiderably beyond this range, that the 
hypothesis accords with experience. The methods em- 
ployed by Tait in his experiments at high temperatures are 
of great interest and importance. One of these was to con- 
struct a cnrvo whose ordinate and abscissa are the simul- 
taneous readings of two thermoelectric circuits whose hot 
and whose cold junctioos are kept at common tempera- 
tores. It is a consequence of the foregoing assumption 
that the curve thus obtained ought to be a parabola. Yeiy 
good parabolas weir in many cases obtained. In some 
cases, however, the corves, so for from being parabolas, 
were actually corves having points of contrary flexure. 
This anomaly led Tait to the discovery of the astonishing 
foot that the Thomson effect tn iron changes its sign cer- 
tainly once at a temperature near low red heat, if not a 
second time near the melting point It was found that 
the inflected curves could be represented by piecing to- 
gether different parabolas. Hence the line for iron in the 

^ Tttm. R. a. S., 1S73. 




method of verification consisted in using along with an 
iron wire a multiple wire of Au and Pd, ihe reaistSBCw of 
whose branches could be modified at wilL It ia easy 
enough to show that the line for the Au-Pd wire ia a 
straight line, passing through the neutral point of Ao and 
Pd, and such that it divides the part of an ordinate lying 
between the Au and Pd lines in the ratio of the respective 
conductivities of the Ao and Pd branches. Thna^ by in- 
creasing ratios of the conductivities of the Pd and An 
branches from up to co , we can make the An-Pd line 
sweep through the whole of the space between Ao sod 
Pd (fig: 65), and thus explore the part of, the Fe line 
lying in the space. We get in this way first one neutral 
point, then two, then one, and then none in our Fe, An-Pd 
circuit. 

Tait has pointed out that, by nsing Ptir and Fe, and Con 
keeping the hot and cold junctions at the two neutral |^ 
temperatures, we get a current maintained solely by the ^^^ 
excess of the heat absorbed in the hotter iron over that dgM, 
developed in the colder. The electromotive force is repre- 
sented by the area inclosed by the part of the zigng on 
the Fe line cut off by the PtIr line (% 65). A similar 
case of thermoelectromotive force wiuiout Peltier efleeta 
may be obtained with three metals, snch as Fe, Cd, €d, 
whose neutral points lie within reasonable limits ^le 
electromotive force in this case is represented by the 
triangle between the three linee. 

Wa rabjoio a table, calculated by Professor Eventt from Tait'a Wt"' 
diagram. The thermoelectric pow«r u given in electromagiKtie ""^ 
(C.G.S.) units, in terms of the temperature (1) in oeDb^rad* 
degrees, bj means of the formnla a -t- 3(, where n and (i have dw 
tabulated valnos : — 





. 


a 




. 


JB 




-1734 

-1139 

- 83S 

- 662 

- 693 

- 709 

- mi 

+ 61 

- 260 

- fil4 

- 221 
+ 1207 


+ 4-87 
+ 3-28 
+ 0'00 
+ 0-65 
+ 1-84 
+ 0-83 
+ 00 
+ 1-10 
+ 075 
+ 1-10 
+ 0'B5 
+ 5'12 




- 288 

- 284 

- 214 

- 288 

- 13« 
+ 
+ 43 
+ 77 
+ 825 
+ 2204 
+ 844S 
+ 80J 


- 4-19 

- 2« 

- 1» 

- i-os 

- 0-»6 
+ 0-00 

- OH 

- 0» 
+ >5» 
+ 6-lS 
-24-10 
+ G-IS 










PtIr(Ep,c, Ir) 
Do. (10 do. ) 
Do. (15 do. 


aS :'■■■:;;:::■'■■.■■■ 








AI 


Pthard. 


Ni to 176' a 

Do.260''toS10*C. 
Do. from S40* C. 




German eiive^ 



1 We need scarcely vam the reader that the reanlta in this taUi 
moit not be nuhly applied to any ipecimeni of the nwtals taken A 
random. The temperatm« limits lie between 18* 0. sad tiO* C 

j It would be extremely interesting to eompara ^ nnlti 



SLIOTBOlfOnyB fORCB.] 



ELECTRICITY 



99 



of absolute measurements of the Peltier effect with Tait's 
**"|^ theory ; but, unfortunately, no data that we know of are 
^^ available for the purpose. It is absolutely necessary for 
Hu^ this purpose to have heat measurements and determina- 
te, tions of the lines of the metals in the same specimens. 
The data of Edlund^ and Le Eoux are quite useless for 
such a purpose. One result of Le Eoux's is, however, 
interesting. He finds for the amount of heat developed 
at the junction BiOu, the values 3*09 and 395 at 25'' C. 
and 100*" C. respectively. Since the neutral temperature of 
BiCu is very high, the Peltier effect ought, according to 
Taif s theory, to vary as the absolute temperature. The 
absolute temperatures corresponding to 25° C and 100"* C. 
are 298* and 373^ and we have 3 95 -=-3 09 = 1-278, 
while 373-^298 a 1*252; the agreement between these 
numbers bears out the theory so far.'^ 
of General ConsidercUiona regarding the Seat of Electromo- 
fcro- iive Force. — Before proceeding to notice the remaining 
^ cases of the origin of electromotive force, in which the 
phenomena are more complicated, and the experimental 
conditions less understood, it may be well to call attention 
to a principle that appears to hold in most of the cases 
already examined. In most of these cases the seat of the 
electromotive force appears to be at the places where 
energy is either taken in or given out in the circuit.' 

It is very natural to ask ourselves what the consequences 
would be if we applied this principle to the voltaic circuit 
It would probably be admitted by most that the energy in 
the voltaic circuit is taken in mainly at the surface of the 
electropositive metal. This admission, taken in conjunc- 
tion with the general principle above stated, leads us to the 
conclusion that the electromotive force resides mainly at 
the surface of the electropositive metal. The absorption 
or evolution of energy at the junction of the dissimilar 
metals is qi;ite insignificant, and we should, on the ^ame 
view, deny that any considerable part of the electromotive 
force resides thera 

This view appears to be at variance with the theory of 
metallic contact, as now held by Sir William Thomson and 
others; and the burden of explaining the experiments made 
by him and others on the contact force of Volta is doubt- 
lees thrown on those who adopt this view. The position of 
such would very likely be that there is an uneliminated 
•ource of uncertainty in all these experiments^ (see above, 
p. 85). On the other hand, those who adopt the con- 
tact force of Volta at the junction of copper and zinc as 
the main part of the electromotive force of DanielFs 
element are under the necessity of distinguishing this 
from the electromotive force corresponding to the Peltier 
effect, which must be a distinct effect, since it is but a 
very small fraction of that of a Danieli's cell 

We are, however, so very ignorant of the nature of the 
motion which is the essence of the electric current that 
the very form in which we have put the question may be 
misleading. If this motion be in the surrounding medium, 
as there is great reason to believe it to be, it would not be 
surprising to find that speculations as to the exact locality 
of the electromotive force in the circuit were utterly wide 
of the mark. The very language which we use implies a 
certain mode of analysing the problem which may be 
altogether wrong. The only thing of which we can as 
yet be sure is that the mathematical equations deduced 

> Uned. Giav., Bd. i § e94. 

* foce the above "was written farther experimental evidence in sup- 
port of the theory has appeared. See Naccari and Bellati, Atti del 
it ItL Veneto di Se, LitL ed ArH, November 1877. 

* MaxweU, vol. L § 249. By ''being taken in," in the case of heat 
for instance, is meant "disappearing as heat and appearing as electro- 
kfaMtic energy. ** In a thermoelectric circuit this transformation occurs 
wbersver there is Peltier or Thomson effect 

«lUzweU,<.e. 



from Ohm's law and other proximate principles are in 
exact accordance with experiment. 

Pyroeleetricity. — Some accoant of this interestinff subject has Pyro« 
already been given in the Historical Sketch at the beginning of this elec- 
article. It will be well, however, to state here some of the conda- tridtj. 
sions of those who have recently investi^ted the matter. It seems 
now to be settled that it is not merely high or low temperature, but 
change of temperature^ which gives rise to the electrical phenomena 
of pyroelectric crystals. The properties exhibited by tourmaline 
may be described thus. One end A of the crystal is distinfi^ishable 
from the other end B by the dissjrmmetry of the crystalhne form. 
A is called the analogous pole of the crystal, and B the antilogtms 
\x>le. When the temperature of the crystal is increasing uniformly 
throughout, the analagous pole is positively electrified and the 
antilogous pole negatively electrified. When the temperature is 
decreasing uniformly throughout, the analogous pole is negative 
and the antilogous pole positive. This law was originally dis- 
covered by Canton,^ but it seems to have been lost sight of again Canton, 
and rediscovered both by Beigman and by Wilcke m 1766. When the Wilcke. 
temperature is uniform, the positive and negative regions are sym- Beig* 
metrically distributed about the central zone of the crystd, which nuuL 
is neutral. If the ends be uneaually heated, this symmetry no 
longer obtains. It must not be forgotten that complications may 
arise from the crystal becoming electrical as a wh(ue by friction^ 
usually positive, like most other vitreous bodies. 

Gaugain* made a series of interesting experiments on the eleo- OaogaiiL 
trical properties of tourmaline, and concluded that a tourmaline 
whose temperature is varying may be compared to a voltaic batteiy 
of great internal resistance, consisting of an, infinite number of cells, 
each of infinitely small electromotive force : so that the electro- 
motive force is proportional to the length of the tourmaline, and its 
internal resistances is proportional to the section inversely and to 
the length directly. He also concluded that the amount of elec- 
tricity furnished by a tourmaline, while its temperature varies either 
way between two given temperatures, is always the same. 

In order to explain the properties of the tourmaline, it has been Thonu 
supposed' that tne crystal is naturally in a state of electrical pola- son's 
rization, like that assumed by Maxwell in a medium^ under the theory 
influence of electromotive force, or more nearly (since no sustaining 
force having an external origin is supposed) like that of a permanent 
magnet. The intensity of this polarization is supposed to be a 
function of the temperature. Supposing the tourmaline to remain 
for some time at the same temperature, a surface laver of electricity 
would be formed, which would completely mask the dectrical 
polarization of the crystal, inasmuch as it would destroy all external 
electrical action. This neutralization would be instantly efifected 
by running the crystal through the flame of a lamp. If, however, 
the temperature increase, then the polarization will, let us say, 
increase, so that the surface electrification no longer balances it. 
We shall thus get polar electrical properties of a certain kind. If 
the temperature decrease, the polarization will decrease, and we 
shall thus get polar properties of the opposite kind. 

In many pyroelectric crystals there are more than one electrio 
axis, so that wo have several analogous and corresponding antilo* 
gous poles. An enumeration of the various crystals in which 
pyroelectric properties have been found, and a discussion of the 
peculiarities in their crystalline form, belongs more properly to the 
science of Mineralogy. Much has been done in this department by 
Kohler,^ Gustav Rose and Riess,* and Hankel.^® For some very in- 
teresting researches by Friedel see Annates de Chimie et de Physiqudf 
1869. 

Friciional Electricity. — In accordance with the eeneral principle Contaot 
laid down at the beginning of this section, we should expect to find of non* 
an electromotive force at the surface which separates two different condvo* 
non-conducting media, just as we have found it at the boundary of tors, 
two different conducting media. The effect of such a contact force 
would be very different nowever in the former of these cases, from 
what we have seen it to be in the latter. In the case of non-con- 
ductors the electricity cannot leave the surface of separation, but 
will simply accumulate on the two sides of it, till the force arising 
from electrical separation is equal to the contact force. On separ- 
ating the bodies, in certain cases, we may carry away with us these 
surface layers of electricity, and it is an obvious consequence of oar 

Principles that the electrifications of parts of the two bodies that 
ave oeen in contact must be equal and opposite. While the 
bodies are in contact the difference of potential between the layers 
of electricity corresponding to very considerable surface density may 
be very small, just as in Volta's condensing electroscope (see above, 
p. 34) ; but when we separate the bodies work is done against the 
electrical attractions, and the potential increases enormously. 

» Phil. Trans., 1759! • Mascart, t it 

' Thomson, Phil, Mag,, 1878, p. 26 ; or Nicholas Cyehpoedia o/tiU 
Physical Sciences, 1860. 
* Pogg. Ann., xvii., 1829. 
» Abh. der Berl. Akad., 1836 and 1843. 
^® Pogg. Ann,, xlix., 1., IvL, 1840-2; also cxzzL, czxzii., 1M7, ftc. 



100 



ELECT BICITY 



[elbotboxotivb pobcx, 



WUcke. 



gave any) of what is called the "frictioaal gencnitioD of electricity. 

All experimenters ar; agreed that eqaal quaotities of poeitire and 
nt^tire electricit; appear in this case as in every other case of 
electrical separation ; an experiment to prove the contrary would 
hav« to be veiy demonstrative indeed ocfore it vould d 



conmlt on this point Faraday's Experimental Seaearcha, series xi. 
ITii. 

The other consequences of our hypothesis are by no means so 
firmly established. One of these is that we ought to be able to 
alranfp non-conducting bodies in a aeries snch that any body 
rubbM vith one below it in the aeries becomes positive, and nibbed 
by one above it negative. 

Many electricians have attempted to establish such electro- 
motiva serins, but the experimental conditions (see the admirable 
remarlia of Riess, ScV/ungseUdrieiUU, § 907) are so complicated that 



materials under definite surface conditions, electromotive 
could be constructed in which ereiy different body would havs a 
fixed positLOD. As it is, the body bearing the same nnme in the 
lists of different eiperimentera was in all probability not exactly 
of Uie same material in all cases, and (we might say certainly) was 
not under the same surface conditions. We refer the reader to 
Riess {l-c.) for an admirable r^mi of the work of different elec- 
tricians in this department. Mascart has given a very interesting 
account of the matter (t. ii. % 634, Ice.) from a more modem point 
of view. From these sources, together with indications in Young's 
Lectura on Natvral PhUoKiphy, the reader will be able to follow 
np the literature of this somewtiat iminviting department of elec- 

We give two instances of friclional electromotive series nhich 
mav be useful in giving the reader a general idea how different 
bodies stanil. 

The following is Wilcke's seriesl (1768) :— Glass, woollen cloth, 
feathers, wood, paper, shellac, white wax, ground glass, lend, sal- 
phnr, metals. 



Considered as evidence for the contact hypothesis, the experiments 
of Peclet seem to be important. He nscil an apparatos which was 
virtoally a Naime's machine (see below, B. lOI), m which the rubber 
could M varied at will. His general conclUBioiis are quite in 
accordance with the contact theory. He found, for instance, that 
for the great 'majority of materials the quantity of electricity gener- 
ated WB9 iudepeudent of the pressure and of the breadth* of tlie 
rubber, and varied as the angular velocity of the cylinder, and it 
even appeared to he the same for rolling friction as for sliding fric- 
tion, so long as the msterial of the rubber was unchanged. 

Besides the case of two non-conductors, we might conuder the 
case of a conductor and a non -conductor in contact. Much of what 
has just been said would apply to this case also, an excellent 
1. eiamplo of which is furnished by a frictional electrical machine of 
the ordinary constrnctiou when the cushions are well furnished with 
amalgam. This is the place to give a short account of these time- 
honoured pieces of electrical apparatus. For a history of them we 
cannot do better than refer to Mascart* (I.e.), who has devoted 
mach attention to the theoiy ai well aa the history of electrical 
mtchines in general. 

A very common form of machine, called Ramsden's, is pictured 
in fig. G6. It consists, like aU other frictional machines, essen- 
tulUy of three parts — (1) the mbbed or moving body, (2) the 
mbbera, and (3) the collectors and prime conductors. In the pre- 
sent instance the rubbed bodv is a disc of glass, which can be 
turned about a horizontal axis by means of a suitable handle. The 
efficiency of the machine depeniu very much on the quality of the 
glass of which the disc is mode. According to Mascart, glass of old 
manufacture is superior to the more modem specimens, owing to 
the amaller proportion of alkali in the former ; it appears, however, 
that the disc improves in most cases with age and use. Many 



1 According to Hiess, the earliert. ' Exp. Ba., 2141. 

• The parchment-lite paper obtained by treating ordinary paper 
with ooncBDtnted lulphuric acid. 

* That is, the dimeniion of the inbber perpendicular to tlie axis of 
rotation, 

' A few notices of the earlier machines will be found in the Histori- 
cal Sketch. 




what costly when huge _ 
a good deal of late, and 
hai great advantages so 
far as its electrical pro- 
perties are concerned ; 
but it has the disad- 
vantage that it warp* 
very readily if heated 
incautiously, and ita 
surface will not keep 
good for any length of 
time. Owing to decom- 
position under the action 
of light, a layer of sul- 
phuric acid forma on the 
surface, after which it is 
Tciy difficult to restore 
the electrical virtue so 
remarkable in the new 
material, although wash, 
ing with hot water oi 
immersion in a blast of 
steam are said to be 
eSective in some degree. 
The rubbere consist < 
two rectangular piec« 
of wood, hinged to sut 
ports attached to tb 
framework of the me 

chine, and fitted with ^ „ „ , • , . , 
springs and screws, so *^<'- B8-— Ramsden s electrieal machine, 
that they can be made to clip the plate with any required pressun. 
The rubbing anrfaces are usually formed of leather, stretched as 
smooth and flat as possible (oiledsilk iasometimea used, but it is not 
so durable}. Before the leather cushions are fit for nee, they must bs 
carefully coated with amalgam. The amalgam most commonly used 
is Kienmayer's, which isa composition of two parts of mereury with 
one of zinc and one of tin. A great variety of different compounds 
of this kind have been used by different electricians, bisulphide of 
tin being a general favourite. The amalgam most bo powdered as 
finely as possi bis, all grit being carefully removed. The cushions an 
then to be lightly smeared with lord, and worked together till tha 
surface is very smooth and the greastDess almost gone ; then the 
amalgam is to be carefully spread over them, and the nirfaees again 
worked together till a uniform metallic surface is attained^ they an 
then ready for use. The amalgam aids the action of the machine in 
two ways, — first, by presenting a surface which is highly nqjative 
lo glass ; secondly, by allowing the negative electricity evolved by 
friction to flow away without hindrance from the points of contact 
In order to secure the second of these advantages stul more perfectly, 
the cushions should be carefully connected by strips of tinfoil, or 
otherwise, with knobs, which can be put to euth during tlie action 
of the machine. 

The collectors are two stout metal forks bestriding the kUm dlM 
at the ends of a horizontal diameter. They are armed, on tlM 
sides next the glass, with rows of sharp points, whieh extend (crasi 
the mbbed port of the disc. The prime conductor in the apecimen 
we are describing forma a metal arch rising over the frunework of 
th« machine, and insulated from the sole by two glass pilUtt. 
Various forms are given to this part of the machine, accor&ig to 
the fancy or convenience of the experimenter- One Important 
thing to be seen to is, that there be no salient point* on it which 
might facilitate the dissipation of electricity by bnuh, oonraetin, 
or swirk discharge. 

After what has been said, the action of the machine reqnim 
little explanation. The disc, electrified positively by contact with 
the amalgam, carries away a positive charge, whoae potential riaci 
rapidly as it leaves the cushion, — so high, in fact, that there ji a 
tendency to discharge to the air, which is prevented by covwing 
the excited parts ol the disc by pieces of oiled silk. Wlieii tha 
highly charged glass comes apposite the points of the eollecto', 
owing to the indkctive action, negative electricity isaneafhim the 
poin^ and neutralizes the charged plate, which at this point il vir- 
tually inside a closed conductor. The remit of this i« that the 
prims conductor becomes positively charged. The nentr^iKd parti 
of the disc now pass on to be mbbed by Uie other cushion, and sa 
on. The electricity goes on accumulating in the prime oooductcr 
nntil the potential is so great that discharge by ■nr[»c« conducticsi, 
or by spark, takes place between the collecton and the enahion, or 
between the collectore and the axis. 

If it is desired to obtain nwttive electricity bom a 7in-h'"t 
with a glass disc, we have slmp^ to connect tha prima condnettf 
to earth, insulate the cushions, and collect the electnci^ tram tbea. 

w« tf.vi. uiii (ii.t ihm. <■ . limi t to the potential to vhieh tlw 



We have said that there is 






roBCK.] 



ELECTRICITY 



101 



elwrge on tliB prime cooductor can be ruied- We can nerer get s 
longer ipark nom the machine than the length of the interral 
between the collector and the cnshion or the axis, aa the case ma; 
be. The limitins potential can, however, be increaied by iugolat- 
log the axil of the machine, or making the azii itself vhoU; or 
partiaUv of ininlating material, and by niing only one robber and 
one collector, and placing them at the eltremitiea of a diameter. 
The machine of Le Roy, oTten called Winter's machine (fig. 67), is 




Flo. G7. — Le Koy'a machine. 
1 this pattern. We get, of course, eeeUrii paribu*, 
only half a* mnch electricity per reTolution with a machine of this 
kind aa with Bamaden's; bat the ipark is longer, in conBenuence 
of the gteater insalation between the casbion (A) and the collector 
(B). 
a The cylinder machine, iIbo called Nairne'a machine, was cue of 
», the first m»chinea in which all the eaaential parta of the modem 



[rictional machin 



n be turned about ahoriiontal axis by a multipljing gei 
_ by means of a n-inch handle i ' ' "■ 
U affixed to one boiiiontiil metal cylinder, 



:e usoal) by i 



idle simply. The i 






another. It is necessary to insulate the 
owing to its proximity to the ends of the conductors. Positive or 
nega&TB electricity can be obtained with equal readiness by insulat- 
ingeither of the conductors, and connecting the other with the earth. 
Those who desire more minute information conccminK the 
fimctioni of the diflerent organs of the frictional machint^. are 
TcferrBd to Uaacart, torn. ii. 3 834, tic. In the aame place will be 
found a dcacription of tite famous machine with double plates con- 
atrncted by Cutbbertson for Van Marum, and still to be seen in 
Teyler's Museum at Haarlem. A diacripliou of another of Van 
Uarnm's machines will be found in the article "Electricity" in 
the Encyclojiadia Metropolilana. We take this opportunity of 
calling Uie scientific reader's attention to that article, which con- 
tains a great quantity of very valuable matter. Much of the work 
of the earlier electricians that wo have been obliged to paas over in 
diencc is fully described there. 

Electric machines have also been constructed of less costly mate- 
rials than glass or even vulcanite — of cloth and paper, for instance 
—for an account of these, see Riess, Bd. ii. g^ 93S, [)37. 

a Many experiments have been made on the electrification of sifted 
powden. We have already, in describing Lichti-nberg's figures, 

1^ alluded to some cases of this kind. Aa a mle, either the results 
are my nncertain, or the conditions of the experiment very com- 
plicated, ao that the experiments are, in most cases, more curious 
than valnable, from a scientific point of view. Such as deiire it 
will find abundant indications of the sources of information in 
Hiesa, Bd. i. H 938 >qq-, =nd Eiury, Mttrop., art " Electricity," 
if 193 tqq. One case of this kind, however, was so famous in its 
day, that we ought to mention it In the year 18(0 ■ workman at 
Newcastle, having accidentally put one hand in the steam which 
«u blowing off at the loTety valve ot a bigh-preaaure engine 
bailer, while his other hand was on the lever oi the valve, cipe- 
rimced a powerful electric shock in his arms. Armstrong investi- 
gated the matter, and was led to construct his famous hydroelectric 
~ "' "" ' " *" ■ 's simply of an insulated boiler 

I, fitted with a teriea of nonlea. 



kept cool by a stream of water. The steam issaet from then 
noiilea and impinges on a coudoetor armed with points for collect- 
ing the electricity. The boiler geta electrified to a high potential, 
and a torrent of dense sparks may be drawn from it The moctUDe 
far surpassed any ordinary electrical marhine in Qxt quantity of 
electricity fumiahed in a given time. By means of it water waa 
decomposed, and the caaes collected separately. It vaa reserved 
for Faraday to trace tne exact source of the electromotive force. 
He demonstrated, by a series of in^uioua experiments, that the 
electrical action arose from the friction of the particles of water in 
the condensed steam against the wood of the nozzles, ' 

Bcmaining Catai, — Of these the most important are atmorplierio vi«mi . 
electricity,' which belongs properly to meteorology, animal elec- ijneona 
tricity, comprehending the study of the properties of the electrical ntults. 
fishes, and the electric phenomena of nerve and muscle. We have 
already indicated the literature of the former subject and the latttr 
belongs, for the present at least, to physiology. Evaporation, com- 
bustion, and ill fact chemical action generally, have been brought 
forward by some experimenters as sources of electromotive force. 
About the last of all there is, of course, in one well-known case no 
doubt As to the eiperimenta generally alluded to under the other 
two heads — in particular, those of Laplace and Lavoisier, Volte, 
Pouillet, and others — there has been considerable difference of 
opinion, and we need not occupy space here with fruitless dia- 
cuasion of the matter.* Similar remarks apply to the electrification 
caused by pressure, cleavage, aud mptare. 

ifackina founS^ on Induction and Conteeiion.' — The oldest Eloctn- 
electric machine on this principle is the electrophorua of Volta, phoms. 
1775. This consists ot a plate of resinous motter (now nsually 
vulcanite) backed by a plate of metal, and a loose metal plate, 
which we may call the collector, fitted with an insulating handle. 
The vulcanite is electrified by flapping it with a cat-skin, the 
collector is placed u]ion it, iminsalated for a moment by toaching 
it with the finger,* and then lifted by the insulating handle, The 
collector plate is then found to be charged (jiositivety) to a high 
potential, and sparks of some len^h may be drawn from it 'The 
explanation of the action of the electropfioruH is simple enough, if 
wo keep clearly in view the trperimtTilal /ael that the surface elec- 
trification of a non-conductor, like vulcanite, will not pass to a 
metal plate in contact with it under ordinary circumstances. If 
the surface density of the electriEcallon Iw very great, discharge to 
the metal may nodoubt take jilace ; and if the collector be kept for 
n very long time in contact with the vulcanite, it is slid that it may 
become negatively electrilied. In the normal state, however, the 
negative electricity of tlie vulcanite remains upon it, and the thin 
layer of air intervening between it and the collector forma tha 
dielectric in a condenser of veir great capacity, so that a quantity 
of electricity coUecls on the lower surface of the condenser very 
nearly equal to that on the vnlcanit*. The difference of potentid 
between the plates is very small {jnst aa in Volta's condensing elec- 
troscope, sec above, p. Si). When the collector is raised it carries 
away the positive charge— the jiotsntial of which, owing to the 
decrease in the caiiocity of the collector, rises enormously. It la 
to be noticed that the potential of the charge on the vnlcanito rises 
to a coTTBsponding extent Tliia remark partly ciplsins the ra- 
markal.le fact that when the collector is kept on the excited 
vulcanite, its electrification may be kept for a long time (for weeks 
under favourable circumstnnces), whereas it spwdily dissipates if 
the vulcanite be left uncovered. According to Riess, the fact that 
a plate of metal laid on an excited piece of glass tends to preserve 
its elcetrificotiou whs discovered by Wilcko in 1762. . 

If eoch time vse charged the collector it were discharged by con- 
tact with the interior surface of a hollow conductor A, it is oovious 
that wc could raise A by a sufficient nnmher of such contoctt to as 
high a potential as we please, provided it were sufficiently well 
insulated. This remark brings Volta's electrophorua into the pre- 
tegory of elec' ' ' - ' 



Tbeearliest apparatus that involved the principle of such machines 
Lppeara to have been Bennefs doublcr.' The principle of this Banusf • 
lay be explained thus. Let A aid C be two ftied discs, doabtar. 



' £zp. RcM., ser. iviii. 2075. 

* See Bims, g 1028 »qq. , and Thomson's papers in Ffpnnt already 
alluded to ; also B«cy. Mel'op., art. " Electricity," § 219, for biblio- 
graphy of older investigators. 

■ See Biess, g§ 943 t^f . 

* This highly-descriptive title U Sir WilUam T 

* In most modem specimens this Is rendered u 
pin, which Is In metallic connection with the metal bKklng of t 
vulcanite, and comes up flush with the surface of the vulcanlt4^ ao 
to loncb tbe collector when it is in liia. 

* Pha. Traiu., 1787. 



102 



ELECTEICITr 



[■UCTROKOTIVB FOBCB. 



, and C in preaence of B be etch equal top, 

and the coefficieDt of inductioo Setween A and B, or C and B, be f , 
Let ua alao anppoaa that the platei A and C are so diitant from 
each other that there is no mutual inBuence, and that f/ U the 
capacit; of one of the diaca when it stands alone. A mnul charge 
Q u communicated to A, and A is ineulated, and B, uninsulated, 
is brought up to it ; the charge ou B will be - -Q. B is noir unin- 
dilated and brought to (ace C, which is uninsulated ; the charge on 
C will be ^Q. C is now insulated and connected with A, which 



'-.-fe(»0- 



A ie now disconnected from C, and here the first operation ends. 
It is obTiouB that at the end of n such operations tliu charge 



Darwin, Cavallo, and Kicholson' devised mechanism for eSect- 

■ ing the moTements which in Bennet's instrumeut were made by 

^™''- h^d. Cavflllo's waa a reciprocatingmovemBiit, batinthemachioeH 

m Ki ' "^ Darwin and Nicholson the motion was continuous and rotatory, 

Nlenol- Nicholson's donbler is a very elegant instrument. A drawing of it 

■"■• is given by Mascart (t ii. g 846 J; the apeoimen there represented 

is very like one which was found among the lato Professor Willis's 

apparatus, and is now in the Cavendish laboratory at Cambridge. 

Xstill more elegant machine is " Nlcholsoc's spinning condenser," 

which bears a remarkable resemblance to the induction machine 

of TSpler.* A description, with a figure, will be found in the 

Eaeydopcedia MOropolilana, art. " Electricity," S 112. 

It is obvious that if any conductor be connected with the part 
of any of these machines corresponding to the conductor A io the 
above description, and the potential of A be raised to any aniall 
positive or negative value,' we can by means of the macMne in- 
crease the charge, and therefore the potential, up Io any required 
omounL We have, in fact, an electric machine which may be used 
for all the ordinary purposes. It woe not with this view, however, 
that these pieces of apjjaratus were first invented, but rather for the 
putpoae of demonstiating smalt electric differences. In this they 
were but too successful, for it was found that it was impossible to 
prevent them from indicating electric differences unavoidably srising 
within the apparatus itself. It was this difficulty no doubt that 
led to their being ultimately abandoned, and for a time forgotten, 
although they were once in high favonr. Of late, however, they 
have been taken up as electromotors with great success. 
Typical The t^ of all these machines is on anangement of the following 
Mnvecto- description. A conductor or carrier C, or a series of carriers, is 
Indnetiva fastened upon the circumference of an insulating disc At the ends 
machine, of a diameter ore two hollow conductors, A and B, embracing the 
disc on both sides, so that twice in the course of a revolution the 
carrier is rirtuolly in the interior of a hollow conductor. Inside 
each conductor ore two springs : one of these is in metallic connec- 
tion with the conductor, and may be called the receiving spring ; 
the other, called the inductor spring, is insulated from the con- 
ductor, and is connected either to earth or with the corresponding 
spring belonging to the other conductor. Snnpose A to be at 
a ■midl positive potential, and B at lero potential; starting with 
C in connection with the inductor spring inside A, it becomes 
negatively electrified oud carries away its cliBTge; it next comes 
in contact with the receiving spring in B, and, being now part 
of the interior of a hollow conductor, it parts with the who& of 
ita charge to B; then it posses on and is charged positively at 
B'a inductor apting ; then discharges to A at A's receiving spring ; 
and so on. 'Ths positive and negative charges are each a little 
increased every revolution, and the difference of potentials accord- 
ingly augmented. This is the principle of Varley's machine' 
(ISSO), and of Thomson's mouse mill and replenisher' ^1867); it 



electricity. The burning match which lie osw In eoqjimetko 
with the portable electrometer acta in the same way. He haa alao 
constructea a water-dropping electric machine on a jitniUf inin- 
ciple. Two streams of water break into drops inside two indncton 
connected with the internal armatures of two Leyden jai^ A and B ; 
the drops from each inductor fall into a receiver connected with 
the other inductor. A very small difference of potential between 
the jars starts or reverses the action of the appaiatna ; in bet, it 
will in general start of itself, and very soon sparks are seen yumti 
between the different parts, and the drops are acattered in all 
directions by the strong electrical forces developed. 

The most remarkable, as well as the most nsefhl, of all theaa H< 
machines is that of Holtz. ' Here the convection is eflected hy m 
means of a disc of glass, which is mounted on a horizontal azia t 
(fig. 68), and can oe made to rotate with considerabls »"g"l" 
velocity by means of a multiplying gear, part of which is seen at 
X. Close behind this gloss disc la fixed another vertical disc of 
glass, in which are cut two windows, B, B. On the aide of the 
filed disc next the rotating disc are pasted two aeetors of paper, 
A, A, with short blunt points attached to them, whiehmnontmto 




Fia G 



-HolU'o 



is virtually that of Bennet's double.. 
TTatar- Closely allied to these machines is Thomson's water-dropping 
dnpjdng potenti^ equalizer. This consists of an insulated reservoir of 
mschins. water, with a long pipe, from the nozzle of which water is allowed 
to break in drops. It is obvious that if the potential of the reser- 
voir be above that of the air surrounding the spot where the water 
breaks into drops, each drop will carry away with it a positive 
charge, and this will go on till the potentials are equalized. This 
device was introduced by Thomson in observations on atmospheric 

' PhiL IV.Hu., 1788. " Fogg. Ann., 1866. 

By connecting the conductor with the podtive or negative pole of 
a nnall galvanic battery, for jnstance. 
^JbuUd, EUti. and Mag., cap. tJx. 

Described In the art. BLicinoMETKB. 



disc (that nearest the reader), the teeth being put oppoaitA tba 
parts of A, A which lie towards the windows. The conba at« 
fixed to metal ahanks, which pass throngh a stont horizontal bar o( 
ebonite. One of these shanks terminatea in a couple of bslli at E, 
and the other carries a sliding electrode D with a long ebdnita 
handle. The framework which carries the horizontal ebonite bar 
and supports the fixed plates, &c., will be uaderatood than tha 

The machine, as originally constructed by Holtl, contained only 
the porta we have described. I'oggendorff doubled all tha paita 
(except, of course, the electrodes U and £). The Csnra icprcMnta 
Ruhmkorff's modification of this constmction. B«£ind the fixed 
disc there is another fixed disc, with windows and armatntea like 
the first, and, beyond that, another movable disc monatedeo tbe 
axis F. The combs are double, as will he teen from tba flgoieb 
To start the machine, D and E are broiuht together, and one of 
the armatures {or one pair), tay^the right hand one, is electrified in 
any manner, let na say positively, and tbe disc act in ntatioa. 
After a little time a hissing noise is heatd, and tbe Tn»i->iin« 
becomes sensibly harder to turn, as if the disc wen moving throngfa 
a resisting medium. If the room be dark, long curved pencila of 
blue light will now be seen issuing from the points in tha left 
band comb, and running along the nmaceof the disc in » direction 
opposite to its motion, while little stars shine upon the pointi of 
the right.hand comb. After this stete has been reached, the halls 
D, E may be separated, and a continuous series of bmsh diachaiga 
will take place between them, even when the distanoa ia very con- 
siderable. If two Leyden jars, L, L, be hnng upon tba eondacton 
which support the combs, the outer coatings being connected by a 
conductor M, then a succession of brilliant and aonoroiu aparki 
will take the place of the brushes. Instead of naing tha two jan 
L, L, we may connect D and E with the internal and eitenwl anna- 
tures of a condenser; it will then be found that, as we '"j""* 
the capacity of the condenser (the angular velodW of tba diae 
being constant), the frequency of the speAa ■^''"""wlitt. whila 
their brilliancy incresses. If we insert a oigh maiitinmi galvaiw 
meter between D and E, it will indicate a cnnent flowing ben I> 



VLIOnOKOTITB FOXCE.] 



ELECTRICITY 



103 



to E, th* iutcoiitT or whicb, under giren atmoqihorie conditioiu 
Mid ginn tMt of Uu machine, will tbtj u the uisalu' velocity, 
baing independent, vithin Tery wid« lunib, of ^a miitance' 
between D and £. 

It i* not difficult to giTe a fcenerul aceonnt of the action of thii 
machine, althongh it ia very hard to Msurn the preciie importance 
of the individn^ parts, veiy alight modificatioiu of which grektiy 
aflect the cfGcieac;. Suppose D and £ in contact ; the right- 
hand amatore, charged +, acta by indaction on the tight-huid 
comb, causing - dectricity to iaane from the pointa upon the disc 
At the aaine time the podtiTe electricity of the right comb passea 
throdgh DE to the len comb, and isaues from its tcelh upon the 
parts of the disc at the other end of the horizontal diameter. This 
+ Blectricity electrifies the left armature -by induction, + electri- 
citf iuoiag from the blunt point upon the further aide of the 
rotating diac The charges thus deposited on the disc are carried 
along, so that the upper half is electrified - on both sides, and the 
lower half + on both sides, the sign of the electriGcatton t>eing 
TSTened as the disc passes between the combs and the srmatutc b; 
the electricitjissaing from the combs and from the armatures. If it 
were not for dissipation in varioos ways, the electrification CTeiy- 
whera wonld obTiously go on increasing ; but in practice a station- 
ary condition is soon attained, in which the loss from tlie arma- 
torea is just balanced by the gain owing to the action of the blunt 
pointa. After this, both sides of the disc are similarly electrified, 
the upper half always - , the lower always + ; -f electricity ron- 
tinnallj issuing l^m the points of the right comb, -electricity 
from the points of the left This is, of course, accompanied by a 
current of + electricity from right to left through DE. 
ijjl^^ The machine of Holtz, as we have described it, is somewhat 
J ^ uncertain in its action in oar moist climat« ; but a slight modifies- 
It**, tioo of it gives excellent results. Upon the axis X is fixed a disc 



. _.h a small rubber attached to the frame of the 

apparatus, and forms a amall electric machine, which keeps the 
annatnrea continually electrified.' The whole it inclosed in a 
glass case, with a beater of sulphuric scid to dry the air. There is 
a machine of thii kind at present in the Cavendish laboratory at 
Cambridge, which nerer faita when the auxiliary appantus ia at all 
in good order. 

A very remarkable phenomenon often occurs when the electrodes 
of Holti's machine are in connection with the aimatuies of a con- 



certain point, and then the condenser discharges along the surface 
of the disc If the experiment be conducted in a dark room, ft Baah 
of light will be seen to pass along the surface of the disc, and 
themifter it will be observed ttiat the long positive brushes have 
shifted from one comb to the other ; after a little the condenser 
ditchafges again, and the brushea will now be seen in their old 
place, and so on. This phenomenon, though interesting to study, 
IS often inconvenient in practice. To prevent it, Holts mtroduc«d 
the disgonal conductor which ia seen on many machines. For an 
account of thia, and for other details concerning these machines, we 
nfer the reader to Mascart, t. ii. g 817 tqq., whose account of 



Btetnntagnetie Ituttutim MaeAitia.—ltia type of these is the 
j_ induction coil or inductorium, sometimes called RnbmkorfTs coil, 
after the gitat Parisian instrument-malter who fiivt brought the in- 
stmmant to perfection. The object of such machines is to obtain 
gnM electromotive force from sources which furnish large qnan- 
titiea of electricity, but have only amail electromotive force. 

The principles on which the action ia founded has been sufficiently 
indicated above in our aection on the induction of electric currents. 
Vs han also given in the Historical Sketch {p. 13) some notices of 
the literature of the subject ; ■ brief enumeration of the rsnuntial 
parts of tha machine ia all that is neceesary here. 

We hare Erst the primary coil — of thick wire and few windinga, 
so as to have a small resistance snd a small coefficient of self induc- 
tion ; tlM secondatY coil surrounding the primary ia of thin wire 
(l^ mm. or ao). with many windings, the lenj^th in large machines 
bein^ often 100,000 metres. In order to avoid the dagger of dis- 
ruptive discharge between parts of the insulated wire, the coil ia 
divided up by insulating septa, so that parts at very different paten- 
tials an separated. In the centre of the primary is placed a bundle 
of iron wires ; this greatly strengthens the action, and a good deal 
depends on the quality of the iron, which ahould be very soft The 
intemptor is sunplj a Isver, worked by the coil itself or by an 
~'~ * it separate from the coil, by means of which tha circuit 



I of the primaty is made and broken automatically. A variety of 
forms have been given to the part of the apparatus ; the intenuph^ 
of Foucault is a very common one.* For some purpoae* a bnak 
driven bv elook-work is tised. The condenser, a very important 

' part of the apuantos, is made of a ntuuber of sheets of tinfoil, 

' interleaved with sheets of oiled silk or varnished paper. One sat 
of leaves of the coudenser is coouected with one side of the break, 
and the alternate set .with the other side. The function of tha con* 
denser is to provide a way tor the electricity when the circuit is 

I broken, and thus to prevent the intense spark of the extra cnmnt 
in the primary, which destroys the contact surfaces of the break, 
and, what is worse, prolongs ths fall of the primary cnirent, aul 
thereby reduces the average electromotive force of the induction 

I Other devices have been tried for efTecting the tame object as tha 
- condenser, such as inserting a fine metallic wire or an electrolyte as 
; an alternative circuit to the bteak ; and these answer the purpose to 
, a considerable extent. An important improvement affecting thia 
part of the apparatus has recently been introduced by breaking the 
primary circuit between the poles of a magnet, the effect of whidl 
I IB that the spark is suddenly drawn aaide (mown out as it were). A 



ABBOLDTB HKUDKSUBIITS. 

We have slready indicated the consideMtiona which determine 
the fundamental units in the two systema that have come into prac- 
tical use. We ought now to explain bow practical atandards can 
be conatmcted to repreaent these fundamental unita, or at least 
known multiples of them. It is necessary to have such atandards 
m order that we may be able to measure electrical quantities in 
absolute mcBsnre bv simple and expeditions methoda of comparieon, 
it being obviously imposaible in practice to make absolute measun- 
mcnts directly on all occaaions. 

EUdmlatiaU SyHem. — By means of Thomson's absolnts electro- Heuan 
meter Ke can determine any electromotive force in absolute measure, of 
In this way Thomson found the electromoUva foroe of Daniell's.B. IL F. 
batteiy to be 'D0374 C.G.S. electrostatical unita.' 

By using the absolute electrometer (see art Ei.iotko1ibtib), or Beslst- 
anotcer that had been compared with it, we oenld by the method anea. 
given above, p. 46, find a resistance (which WM hugs enough to 
Buit tha method) in electrostatical measure. 

Then, having standards of electromotive force and resistance, we Currenl 
could easily measure a corrent in electrostatic meaaore by applying 



law. The same thing might be done by conatmcung the 

standard of i^oantity. which ia the charge on an isolated sphen of 
unit radius charged to uuit potentiaL By comparing the throw 
of a nivanometer when unit quantity is dia^hai^ed through it with 
the dedection produced by any current, we could determine tha 
latter in absolute meaaure by observing the time of oKillation of 
the galvanometer and the logarithmic decrement of its oscillation 
(see Maxwell, vol. ii. g 710). 

Among the absolute measurements in the present system of units, IH- 
we must not omit to mention Sir Wm. Thomson's determinati<ms elw 
of the dielectric atrength of different thicknesses of air. From str 
these, and from the measurement of the electromotive force of 
, DanieiraceLl just mentioned, he concluded that a Daniell'a battery 
I of 5510 elements would be competent to produce a spark between 
I two slightly curved metallic surfaces at ) of a centimetre asander 
I in ordinary atmospheric air.' 

EUctnmagnetic Syaltm. — The great n^jority of the absolute Gle 
determinations hitherto made have reference to this system. W< ~ 
! make no attempt here to inatructthe reader concerning the detaQs ot meMONk 
I this subject; such an attempt would lead us into techmcal jarticnlais 
intelligible only to a few scientific men. We are fortunate, however, 
in being able to refer the English reader to two books which contain 
in a coBected form all, or nearly all, the reouiaite information, viz. 
Maxwell's EUdricity amd MaffntHtm, and the collected Report* of 
, the Committee of the British Association on Electrical Standards.' 

As a specimen of the t}ieorelieal consideratjonl involved, the Resist- 
reader may take Maxwell's method for determining the coefficient anca. 
of self-induction of a coil (given above, p, 80). If we know the 
value of L (iu centimetres} from calculation, then equation (33) 
I might be ns^ to find x in absolute measure. This would not be a 

Sracticable method, inasmuch as the calculation of L wnuld be 
ifficult if not impossible ; we might, however, determine L by 
comparison* with a coefficient of mutual induction which coiUd be 
calculated. 
The earliest abeolnte measurement of the naistanca of a wire [by Siidi- 



> We spMk of reaiitonCM ot 1 to IU,DDO or 100,000 ohms. 

* "Die Una of dlvlsiou la not boriiontsl, however, it, lnde«l, it be 
■lactly a diameter. Bee Uaecart. 

* Owipare Canfs machine, Uaecail, t IL g 8U. 



* See Wiedemann's Oalv., or Dn If once], Kotia tur FAppanU da 
RuhnJcarff, 

' EeprirU 0/ Paptn, g SOS, 4c ' Ittprini b/ Papert, |S40. 

' Such as with to go deeply into the matter most read tiie Jfoos- 
batimmungai of Weber. 

* Maiwell, vol. IL { 7Sa 



104 



ELECTRICITY 



[absolute in&JLSUBKMXHTB. 



Kircbhoff in 1849) was of the kind just allnded to; that is to say, 
it involved the comparison of a resistance with a coefficient of 
mutual induction, the time measurement being that of the period 
of oscillation of a galvanometer. 
Weber. Weber used two methods, — (1) the method of transient currents, 
in which he measured the throw of a galvanometer caused by the 
current from an earth inductor of known area when it was turned 
about a vertical axis, so that the number of the earth's lines of 
force through it increased from zero to a maximum; and (2) the 
method of logarithmic decrements, in which he observed the time of 
oscillation and the logarithmic decrement of a magnet in a galvano- 
meter of known constant. In the last of these two methods the 
horizontal component of the earth's horizontal force comes in 
directly, and the magnetic moment of the galvanometer magnet 
must be determined, which is a matter of great difficulty. 
BL A« The determination of the British Association committee was carried 

com- out by Messrs Idaxwell, Balfour Stewart, and Fleenung Jenkin, and 
mittee. the result of it was the construction of a standard called the ohm, 
which professes to represent a velocity of an earth quadrant per 

cm. 

second (lO*— --). — The method they used is due to Sir "Wm. Thom- 
sec 

son. It consists essentially in causing a coil of wire of known 
dimensions to rotate about a vertical axis, and observing the deflec- 
tion of a magnet of very small moment suspended at its centie. 
Kohl- In a recent determination, F. Kohlrauscn^ has combined the two 

rausch* methods of Weber, and thereby avoided some of the difficulties 
which arise in either method used by itself. His value for the 

Sarth quadrant 
resistance of Siemens's mercury unit is 0*9717 — g^ i . 

According to Dehms and Hermann Siemens, the resistance of the 
coil called the ohm is equal to 1 '0493 mercury units. According 
to Kohlrausch, therefore, the actual British Association standard is 

1 '0196 '^rtn quadrant ^^ ahgoj^te measure : or, in other words, the 

Second 
determination of the British Association Committee is out by nearly 

2 per cent. 

Loiene. Lorenz* has, still more recently, made a determination of the 
value of the mercury unit in absolute measure. He causes a copper 
disc to rotate inside a coil of known dimensions. The two enos of 
a circuit C are kept in contact with the axis and circumference 
respectivelv of this disc. At two points A and B of C, the resistance 
between which is R, are attached the two terminals of the coil of 
wire, in circuit with which is also a battery. A sensitive galvano- 
meter is placed in the circuit C, and the angular velocity of the 
disc is adjusted till this galvanometer indicates no current. If n be 
the number of revolutions per second, and E the electromotive force 
of induction per unit of inducmg current, calculated from the 
dimensions of the coil, then the resistance R is equal to nE in 
electromagnetic measure. 
The result obtained by Lorenz for the value of the mercury unit 

18 -9337 ^^1? q^^^*^"^ ; this would make the value of the B. A. 
Second 

stodard -9797 ^ 'i"'^''*"* . 

Second 

There is thus considerable discordance between the different 
results. It is a curious fact that the mean of the result of Kohl- 
rausch and Lorenz gives for the value of the B. A. standard 

.^ggg Earthjuadrant ^^^^ determinations are, however, in 

Second 
progress, and it is to be hoped that the doubt which hangs over 
the matter will be dispelled/ 
Cblori- Besides these methods, there is yet another of a totally different 
metric character, originally suggested by Thomson in 1851, in his paper 
method, on the " Mechanical Theory of Electrolysis.*' This method con- 
sists in measuring the amount of heat developed in a wire by a 
current the square of whoso strength is known in electromagnetic 
measure. If we know the mechanical equivalent of heat with 
sufficient accuracy, we can calculate from these results the resist- 
ance of the wire in absolute measure by means of Joule's law. 
Measurements of this nature have been made by Von Quintus 
Icilius,* Joule," and H. Weber.« 
Current We can, by means of a tangent galvanometer, find the value of 
any current in electromagnetic measure (see art. Galvanometer). 
If the resistance of the circuit be found, by comparison with the 



^Pogg. Ann., Ergbd., 1873. * Pogg. Ann., 1878. 

' Since the above was written, an account has appeared of a new 
determination by H. Weber of Zurich. His results, from three distinct 

methods, differ by less than y^» ^^^^ g^^® '^^50 x 10» — for the 

Siemens unit. This would make the B. A. unit 1 '001 4 x 10» ^i?^ 

soc. 

* Pogg, Ann., 1857. 

^ Brit. Assoc. Rep., 1867. 

^ DisseriaUan, Leipsic, 1863, quoted in Wiedemann, Bd. il. § 1109. 



ohm or other absolute standard, we can determine the value of the 
electromotive force in the circuit by Ohm's law. Measurements of 
this kind have been made by Bosscha,' by Von Waltenhofen, F. 
Kohlrausch, and Latimer Clark. The results of Kohlrausch' for 
the cells of Daniell and Grove, when no current is passing, are 
1138 xl0> and 1942x10^ C.G.S. units respectively. Latimer 
Clark ' gives 1110 x 10^ and 1970 x 10^ for the same constants. The 
results, of course, depend on the constitution of the cells. 

Taking the number of electromagnetic units in an electrostatic 
unit to be 3 X 10^^ we ^et from Thomson's electrostatic measure- 
ments for the electromotive force of Daniell's element 1120 x 10* in 
C.G.S. units. ^^ The agreement among the different results is to 
far good. 

The determination of the electrochemical equivalent of some 
elementary substance in this system of units iS of great import- 
ance. Determinations exist by Weber, Bunsen, Casselmann, Joule, 
and F. Kohlrausch. The result of the last is no doubt the best, 
as he combined with his voltametric experiments a determination 
of the horizontal component of earth's magnetic force, which is the 
most uncertain factor in the result According to his result, one 
C.G.S. unit of electricity deposits '011363 (d: '000002) gm. of silver. 
From this we get for the electrochemical equivident of water 
'0009476. 

Jiatio of SUctrosUUic to Electromagnetic Unit. — If we measure 
the same quantity of electricity first in electrostatic and then in 
electromagnetic measure, the fundamental units of mass, length, 
and time being the same in both cases, the ratio of the two 
measures will vary directly as the magnitude of the unit of lenj^, 
and inversely as the magnitude of the unit of time adopted. Tliis 
ratio may therefore be regarded as a velocity which will remain the 
same whatever three fundamental units we adopt. ^^ 

This velocity was found by Weber and Kohlrausch by the direct 
process of measuring the same quantity of electricity, first in terms 
of the one unit and then in terms of the other. This result was 



Electro- 
chcmiei 
eqiiiTi> 
lent 



31xl0» 



cm. 

SCO* 



Five other methods will be found described by Maxwell, voL vL 
§ 768 9gq, Two of these have actually been cai'ried into execn- 
tion,— one by himself, the other by Sir Wm. Thomson. The 

results for the fundamental velocity are 28*8 xlC ^^ and 

sec. 



Metnr 

meotd 

gie 

fundi- 

mentil 

velocity 



Weber 
and 
Kohl. 
ranadL 

ICaxwdl 

Thorn- 



I 



28 '2 xl(fi SUL respectively. 

Theobies of £leotrical Phenomena. 

Throughout this article we have limited ourselves as much as Speenli- 
possible to an exp|Osition of the experimental facts of electricity, tive 
Where mathematical developments have occurred, they have tbeoiMi, 
in most cases been simply deductions from some principle or&c 
principles well established by experience. To have ma^ our 
survey of the present state of electncal science complete, we ought 
to have added a section on the different attempts which have 
been made by the doctors of the science to penetrate a little 
farther into the secrets of the hidden mechanism by which 
electrical phenomena are brought about But any attempt at 
a review of this kind must be relinquished. We refer the 
reader to our indications of the literature (Historical Sketch, 
. 10). The most important work in this department lies at hand 
or the English reader in Professor Clerk Maxwell's Treati$e on EUc' 
tricUy and Magnetism.^* Particularly important are his theory of 
electric displacement and its application to statical as well as to 
current electricity ; his investigation of the stresses in the medium, 
by which the electrostatical forces on the one hand, and the electro- 
magnetic forces on the other, may be produced ; the application of 
the theory of displacement to the case of electrical equilibrium 
when the dielectnc medium is not everywhere the same; the 
dynamical theory of the electromagnetic field ; and the electromag- 
netic theory of light. Maxwell ^ves, at the end of his woric, a miSx 
instructive summary of the different speculative theories. The 
student who desires to pursue this department farther will do well 
to master this summary at the outset (O. CH.) 

^ Whose result has already been quoted. It is too low, on aoooont 
of polarization. 

^ Pogg. Ann,, 1870, andEiigbd., 1874. 

* Everett, Illustrations of C. G. S, System qf Units, § 125, or /oiim. 
Soc. Tel. Eng., 1873. 

>« Everett, I.e. 

" Maxwell, Elect, and Mag., vol. IL § 768. 

'' We have followed throughout the views expounded In this woik; 
and we are also under great obligations to its author for his advios on 
many points. For aid in collecting facts we are Indebted mainly to 
the works of Riess, Wiedemann, and Mascart Without their aid 
many sections of this article could not have been written. "^IHedA- 
mann's treatise, in particular, lightened our task by the extent of its 
information and the profusion and aeewracy of its referenees to oeigl- 
nal authorities for the facts in electrical science. 



ELECTRICITY 



105 



Index. 

The figures refer to the pages. 



Ateohite measoremenU, 103, 
104; hlitoryof« (ToaiM, Fcfter, 
B.A. Committee, Ac., 15. 

Aecomolator, theory of, 34. 

AlteriMting discharges with 
Indnctoriom and Leyden 
Jar, «aL 

Afli^^ dectrodynamics, 10. 

Ampirit law, 70; experiment 
tal airangements for show- 
ing electrodynamical action, 
7a 

Aw^iret theory, sketch of, 74; 
generalization of, 7&. 

Are, rdtaic, 6& 

Battertoa, 92-94; history of, 
13 ; one-flaid and two-fluid 
—oxidising agents in— local 
actioQ— polarization, A&, 93. 

Battery of Leyden jars, 95. 

Boond and free electricity, 35 

Bowl, spherical, distribation 
on, Thonuon, 33. 

Brash, 63. 

Capacity, coefficients of, 27. 

Cascade jars in, 85. 

Cell of Danielle different mo- 
diflcations of, 93, 94; of 
Qro9t, Bumsen, Ac., 94. 

Chemical affinity, electrical 
measure of, /ou/e, 92. 

Clrcnit, linear, Ohm*i law for, 
42; action on, in magnetic 
field, 68. 

Circular current, magnetic 
action of, 71. 

Condensing electroscope, 34. 

Conduction, (7ray, 4; general 
equations of, 41. 

Condnctirlty boxes, 45. 

Conductors, network of linear, 
Kirchfiof, 43; conjugate, 43. 

Conjugate functions, 33. 

Conservation of energy, /ou/c, 
Ac, 14. 

Contact force, general law of, 
83, Fo/fa*« experiments, 83; 
Voita's Uw, 83; KM- 
raiuchi's research^, 83 ; 
HamtH's experiments, 84; 
nomtan't demonstration, 
85; Cti/Um*» experiments, 
85 ; uncertainty concerning, 
85 ; from polarisation, 86. 

Contact of conductor with 
non-conductor, 100. 

Contact of non-conductors, 99. 

Conrection, electrolytic. Helm- 
Ao/rt, 87; of heat, electric, 
Thoiiuom, 97; JhU't conjec- 
ture concerning, 97. 

Conrectire discharge, 64, 66. 

GooTecto^oductiTe macliines, 
Holtt, l^er, Varttjf, Thorn- 
«m, 101, 102, 103. 

Coutomb^ 9; his torsion ba- 
lance, 18. 

Corrrat, electric, general phe- 
nomena and measure of, 40. 

Currents, mutual action of, 
when parallel and when 
iodlned, 70. 

Deeompositlon of alkalis, Davp, 
9 ; of water by electric cur- 
rent, Jfieholion and Ceurlitie, 
9 ; by electric spark, 9. 

Dltiectric ttrength of gases, 
Ac, Harrit^ Riest^ Ac, 60; 
effect of pressure, Ac, on, 
Harrii^ 61; Faraday's re- 
searches on, 61; Wudemann^ 
Riklmanm^ 61 ; at high pres- 
Borea, 62; minimum for 
vaennm, 62. 

DlfferantUl galranometer, 43. 

IHKharge in fluids, 65; in 



solids, 66; In gases, mag 
netic action on, I>e la Bite 
and PlUdLtr^ 74 

Disruptive discharge, 59-66; 
theoretical considerations 
00, 60; progress of, 62. 

Distribution, electrical, Cout- 
lomb^ 19, 20, 22-24 ; gene- 
ral problem of, 27. 

Donbler, Bennet't^ Darvin^ 
Cavalio, and Jficholson, 102. 

Earth's action on suspended 

current, 72. 
Electricity, positive and nega- 
tive, Dt^fay^ 4; theory of, 
17. 
Electrics and non-electrics, 

Qilbert and Boyle^ 3. 
Electrodes, temperature of, in 
discharge through gases, 
64. 
Electrodynamics, theory of, 
Ampire^ Weber^ Neumann^ 
JJelmhoUtt Maxvtll, 10, 
66-74. 
Electrodynamometer, use of, 
in measuring electrolytic 
resistance, 49; Weber's ex- 
periments with, 71; Am- 
phre's theory verified by 
means of, 71. 
Eiectroklnetic energy, 81 ; 

Thomsons theory of, 76. 
Electrolysis, Faraday^ Ac, 13, 
Electrolytes, Ohm's law for, 
47; Faraday's law of con- 
duction for, 47; his law of 
electrochemical equiva- 
lents, 47; polarization and 
transition resistance with, 
47 ; resistance of, Uorsford^ 
Beets, Paaitow, Kohlrausch 
and yippotdt^ Eveing and 
ifacgregor, 48-60. 
Electromagnetic engines, his- 
tory of, 10. 
Electromagnetic rotation, 72; 
discovered by Faraday, 10 ; 
his apparatus, 72: Ampkres 
theory of, 78 ; different ap- 
paratus for, 73; of fluids 
73 ; of electric discharge, 74. 
Electromagnetism and electro- 
dynamics, 66-75. 
Electromotive force, origin of, 
83-103; measurements of 
Poggendorff and Clark, 86 ; 
dynamical theory of, Thom- 
son^ 90; calculated from 
chemical data, 90 ; limit of, 
in electrolysis, 90 ; question 
as to seat of, 99. 
Electromotive series — two 
metals and one liquid, two 
liquids, one metal and two 
liquids, Ac, 86. 
Electrophorus, VoUa, 101. 
Electrostatical theory, recent 
history of, Orctn, ThotfisoH^ 
Oauss, Ac, 15. 
Electrortatics, mathematical 

theory, 24-86. 
Electrostatics, experimental, 
recent history of. Faraday, 
Harris, Riess, Ac, 14. 
Element of circuit, action on, 

in magnetic field, 68. 
Ellipsoids, distribution on, 30. 
Energy, eiectroklnetic, of two 

circuits, 76. 
Energy, laws of, in voltaic cir- 
cuit, Joule, 89 ; Favrt and 
Silbermann, 89; Thomson^ 
9a 
Energy, transformations of, in 

electric circuit, 54, Ac 
Equilibrium, electrostatic, con- 
dition of, 26. 



Faraday, induction of electric 
currents, 11. 

Figures of Lichtenbergt of 
Karsten, 66. 

Fishes, electrical, 8. 

Floating battery of De la Rive, 
72. 

Force, electric, laws of. Cou- 
lomb, 20, 21. 

Force, electrortatlc, for any 
displacement, 29, 80. 

Franklin's researches, 6; por- 
trait experiment, 58. 

Friction of powders, Ac, Arm- 
strong's machine, 101. 

Frictional electricity, contact 
theory of, 99. 

Frictional electromotive series, 
Wileke, Faraday, Riess, 
100 ; Peclefs experiments, 
100. 

Frictional machines, Ramsden, 
Le Roy, Naime, 100, lOL 

Galvanometers, history of, 13 ; 

differential, 43. 
Gas battery, Orore, 87. 
Gases, rarefied, light effects in. 

64. See also Dielectric 

strength. 
Glow, 63. 

Glowing of wires, 58. 
Core's railway, 58. 
Greens theorem, 29. 

Heat, local, at electrodes. 
Joule, 90 ; Favre and Sil- 
bermann, Bosseha, 91 ; 
theories of Thomson, Joule, 
Bosseha, 92. 

Heating effects, 55-59 ; gene- 
ral law of, 55; from dis- 
charge of statical electricity, 
56 ; from constant current 
in metals and electrolytes, 
56 ; reversible at junctions. 
Ac, 57 ; general theory of, 
57. 

Images, electric, Thomson, 82 ; 
formed by surface electri- 
fication, 66. 

Induction, Cantons discovery, 
7 , history of, 11 ; coefficients 
of, 27 ; through a surface, 
25; between two fixed cir- 
cuits, 81 ; in masses of 
metal, Pltieker, Foueault, 82. 

Induction of electric currents, 
77-83; Faraday s laws and 
MaxwtlCs statements, 75; 
deduction of laws from 
conservation of energy by 
HelmhoUz and Thomwn, 75 ; 
of two circuits, 76 ; coeffi- 
cients of, 76; Neumann's 
theory of, 76; Lens's law 
of, 76; effect of material 
and thickness of wire, 76; 
effect of medium, 77; ex- 
periments with electro- 
dynamometer, ITfftfT, 77 ; 
Feud's researches on, 77; 
unipolar, 77, 78; coils with 
iron core, 78; physiological 
effect of currents, 78; by 
statical discharge, 78; cur- 
rents of higher orders, 79. 
Induction, self, 76; Jenkins 
observation, 79; Faraday's 
researches and theory, 79; 
Edlund's resulU 79 ; coeffi- 
cient of, to measure, ifax- 
ire//,80; calculations and ex- 
periments of Helmholts, 80. 
Induction coil or inductorium, 

103. 
Inductive capacity, specific, 
I Faraday, 36; Siemens, Oau- 



gain, OUtson and Bartlay, 
Bolttmann, 87; SAiller, 
Silow, Bolttmamn, 88. 

Inducto-convectlve machines, 
101. 

Inversion, electric, T^muon, 
83. 

Iron, action of soft, 75. 

Joule's law for heating effect, 
56. 

Kite experiment, Franklin, 6. 

Lens, law of induction, 11. 

Level surfaces, theory of, 25. 

Leyden jar, Muschenbroeck, Ac, 
5; theory of, 35. 

Liehtenberg's figures, 66. 

Light, electric, Ouericke, 4; In 
Torricellian vacuum. Hawks- 
bee, 4 ; phenomena, 59. 

Lines of force, theory of, 26. 

Local action in batteries, 98. 

Magnetic pole, action of cur- 
rent on, 70. 

Magnetism of rotation, Arago's 
discovery, 11; his experi- 
ment, 82; Faraday s ex- 
planation, 82; mathemati- 
cal investigations, 83. 

Magnetization by current, 
Arago and Davy, 10. 

Magneto-electric machines, 
Pixii, Ac, 12. 

Manee's method of measuring 
battery resistance, 50. 

Measurements, absolute, 103- 
104. 

Mechanical effects, 65. 

Medium, insulating, 86-4a 

Melting of wires, 58. 

Multiple arc, 43, 

N^mann, F. £., theory of In- 
duction, 11. 

Oersted, magnetic action of 

current, 10. 
Ohm's law, 40-43 ; history of, 

12 ; for electrolytes, 47. 
08Cillations,eIectrical, Thomson, 

81 ; experiments of Fedder- 

sen, Schiller, Ac, 82. 

Peltier effect, 57. 

rhenomena, fundamental, 16. 

Physiological effe^ of electric 
currents, 78. 

Toints and edges, density at, 
81. 

Poisson, 9. 

Polarization, history of, 14; 
varieties of, 86; in batteries, 
93; by gases, 87; maximum 
of, on what it depends, 88; 
decay of, 88; numerical 
results concerning, 88; un- 
polarizable electrodes, 89. 

Potential, electrostatic, theory 
of, 24-27; coeflScicnts of, 
28; faU of, in voltaic cir- 
cuit, 42. 

Potential of magnetic shell, 67; 
of two circuits and of circuit 
on itself, Neumann, 76. 

Potential energy, theorem of 
mutual, 28. 

Potential energy of system, 29. 

Pyroelectridty, Canton, WUcke, 
Bergman, Ac, 96; early 
history of, & 

Quanaty, electric, 18, 19. 

Residual discharge, KoM- 
rauseh, 89; Maxwell, Hop- 
kinson, 40. 



Resistance, measurement of, 
43-46; history of meaaiir»- 
ments, 18; of battery, 50; 
specific, general table of, 
53; of transition, 87. 

Resistance in general, on, 51 ; 
of metals and alloys, data 
concerning, 51; of electro- 
lytes, data concerning, 52. 

Resistance boxes, 45. 

Resistances, measurement of 
small, 45, 46 ; of great, with 
electrometer, 46. 

Rheostat and rheochord 45. 

Screena, electrical, 29. 

Shell, magnetic, representing 
the action of a current, 67. 

Sine Inductor, experiments 
with, 48, 49 

Solenoid, 7L 

Spark, 62. 

Sphere with given force, 81. 

Spheres, two Influencing, Pois- 
son, 81. 

Standards of resistance, 44. 

Surface electrification, 6a 

Synthetical method, Oreen, 82. 

Systems, Internal and exter- 
nal, 29. 

Tension defined, 60 ; limiting 
60; positive and negative, 
61,62. 

Theories, speculative, of elec- 
trical phenomena, 104 ; con- 
tact and chemical, of voltaic 
circuit, 14. 

Theory, one-fluid, Franklin, 6; 
one-fluid. Cavendish, 6i one- 
fluid, jEpinus, 8; two- fluid, 
Symmer, 7, 

Thermoelectric diagram, Teiit, 
97. 

Thermoelectric inversion. Gum- 
ming, 96. 

Thermoelectric series, Seebeek, 
94. 

Thermoelectricity, 94-99; hia- 
tory of, Sesbeck, Cumming, 
Peltier, Thomson, Ac, 11; 
Seebeck's discovery, 94. 

Thermoclectrometer, Harris 
and Rteu, 55. 

'Ihermoelectrorootlve force, 
order of magnitude of, 95 ; 
results of Magnus, 95; 
effects of strain, Ac, on, 
Thomson and Le Roux, 95; 
in circuits of one metal, 96 ; 
Tlumson's theory of, 96,97; 
TVi^ri addition to Thonuons 
theory, 97 ; his experiments 
and results, 9a 
Thomson effect, 57, 97. 
Torsion balance of Coulomb^ 

la 

Transmission of electricity, 

Watson, a 
Tretelyan rocker, 58. 

Unit, electromagnetic, of curw 
rent strength, 71 ; of elect- 
romotive force, 75. 

Units, electrosutic and elec- 
tromagnetic, 41. 

Vector potential of magnetle 

shell, 68. 
Velocity of electricity. Wheat' 

stone, 65. 
Volatilization of wires, Ac, f%. 

Water-dropping electric ma- 
chine, Thomson, 102. 

Weber, 10; his experiments 
with electrodynamometer, 
7L 

Wheatstone's bridge, 4i. 

VIIL — 14 



106 



ELECTROLYSIS 



ELECTROLYSIS. A very slight acquaintance with 
the phenomena of conduction of electricity by different 
bodies shows us that conductors may be arranged in two 
very distinct classes. In one the passage of electricity 
produces no change in the chemical composition of the 
substance, unless indeed the electromotive force be so great 
that disruptive discharge occurs, or so large an amount of 
heat is generated that chemical effects ensue; the con- 
ductivity diminishes slowly as the temperature rises, and 
if the resistance of the rest of the circuit be small compared 
with that of the substance under consideration, an amount 
of heat is produced in tlie latter equivalent to the energy 
expended by the sources of electricity. To this class of 
conductors probably belong all solids, with the exception 
of hot glass, which conducts with decomposition at a 
temperature below the fusing point. The conductivity 
differs enormously in the different cases ; those which con- 
duct most readily are the metals, alloys, the chemical 
elements generally, and some few metallic oxides and sul- 
phides (Faraday, Exp. Res,, 440, ser. iv.; Skey, Chem. 
NewSy zxiii.). Besides fused metals Faraday added one 
liquid, fused periodide of mercury, to the list, but subse- 
quently gave reasons for considering that it was misplaced 
{Exp, Re$,, 691, ser. vii.). The other class of conductors 
presents a remarkable contrast to the one just described. 
In these the passage of electricity results in the chemical 
decomposition^ of the substance of the conductor at the 
points where the electric current^ enters and leaves the body ; 
a rise of temperature produces in such bodies a very con- 
siderable increase in the conductivity, but the specific resist- 
ance of even the best conducting among them is always very 
great compared with that of the metals. (For details see 
article Electricity, p. 46 sqq,) Only part of the energy 
of the circuit is spent in heating the conductor, as a trans- 
formation of energy takes place in the chemical and mole- 
cular actions at the points where the current enters and 
leaves the conductor. 

It is the behaviour of the second class of bodies under 
the influence of the electric current that we have now to 
discuss. The physical side of the subject has already been 
considered in the article Electricity; so we shall 
principally confine our attention to the phenomena of 
electrolysis which bear on the laws and principles of 
chemistry. Before going further it will be necessary to 
introduce the technical terms which have now become 
familiar, and, in order to be definite, we will consider 
somewhat closely a particular instance of electrochemical 
decomposition of the simplest type. 
Typical The cell in which the action takes place consists of a 

U^r ^^® ^^^ ^^ ^^^^ ^^®^ ^^^* ^^^® * V-shape ; into this is 

^Q^ introduced some silver chloride, which is kept fused during 

the experiment ; into the liquid in one leg of the tube is 

dipped a platinum wire connected with the negative pole 

(zinc) of a battery^ of 3 or 4 Grove's cells, and into that in 

* We have not space here to discuss whether or not conduction in 
electrolytes is always attended with decomposition, although the 
question has engaged the attention of many Yrriters on the subject. 
The reader who wishes for information upon the point may consult 
Faraday, Exp. Jtet. 966-987i, ser. viii. ; Despretz, CmnpL Rend., 
t xliL p. 707 ; De la Rire, Archives, t. xxxii. p. 88 ; Logeman and 
Van Breda, PhiL Mag. [4], viii. 465 ; BufF, Ann. d. Chem. u. Pharm., 
Bd. xciv. s. 15 ; Foucault, Compt. Rend., t. xxxvii. p. 580; De la 
Rire, Ann. de Chimie, [8], t. xlvi. p. 41 ; Favre, Campt. Rend., Ixxiii. 
p. 1463; Hclmholtx, Berlin AfonaUbericht, 1878, Nachtrag zura 
Juliheft; and, for a summary of results, Wiedemann, Oalv., Bd- i. 
§814-316, and Nachtrag, 86, § 884. 

' The standard direction of the current is taken, as usual, to be 
from the copper through the wire to the zinc of an ordinary linc- 
copper celL 

* It b not necessary to use a voltaic battery, — any source of elec- 
tricity serves, — but either a voltaic or a thermoelectric battery is 
njually employed, since these so conveniently supply a large quantity 
of electricity, with an electromotive force sufficient for the purpose. 



the other a piece of graphite or gas carbon connected with 
the positive pole of the same battery. We will suppose a 
galvanometer introduced into the circuit, and that the 
current strength as indicated thereby is, roughly speaking, 
constant, so that the quantity of electricity which passes 
can be measured roughly by the time occupied in passing. 
After the circuit has been closed a short time, bubbles of 
chlorine will begin to come off from the carbon, while pore 
silver is deposited upon the platinum wire, but except at 
these points no alteration will take place at any part of the 
fluid. If the platinum wire with the attached silver be 
weighed at intervals, it will be found that the amount 
deposited after the current has become constant is propor- 
tional to the time, i.e.y to the amount of electricity which 
has passed through the liquid. The same will be true of 
the chlorine if collected in the other leg of the tube, due 
allowance being made for the small bubbles retained by the 
carbon, &c. And the amount of chlorine will be chemically 
equivalent to the amount of silver; thus for every 108 
grammes of silver on the platinum there will be 35*5 
grammes of chlorine set free in the other leg of the tube. 
Moreover if the current be varied by varying the number 
of battery ceUs, it will be found that the amount of decom- 
position in a given time is proportional to the current^ that 
is, again, to the quantity of electricity which traverses the 
substance. 

Faraday, who was the first to define the laws which Noow 
hold in electrochemical decomposition, introduced, for the ^^^■*"' 
sake of precision, a system of nomenclature which has since 
been generally employed. Wishing to regard the terminals 
corresponding, in any similar case, to the carbon and 
platinum in the above experiment merely as the " doors *' 
by which the electricity enters and leaves the liquid, he 
denominated them electrodes, and, comparing the " path " 
of the current to those of the currents which may produce 
terrestrial magnetism, and hence to the course of the sun, 
he called the homologue of the carbon (where the current, 
so to speak, "rose," or entered) the anode^ that of the 
platinum (where the current "set," or left) the cathode. 
The component parts, no matter how complex, into which 
the liquid was decomposed, corresponding to the Ag and 
CI of the above, received the name of " ions " — ^that com- 
ponent which went doion with the current to the cathode, 
and there either was set free or combined with the cathode 
or the surrounding liquid, being the cation, and that which 
went up against the current, and appeared or promoted some 
chemical action at the anode, the anion. Moreover, the 
substance decomposed was called an electrolyte^ Kudi the 
process itself electrolysis. (Faraday, Eaop. i2«L, 662 s^.) 

The phenomena which occur at the electrodes when the 
ions there set free react upon the electrode or the snrround- 
ing fluid, so that the resulting products of electrolysis are 
not the ions themselves, are called secondary txctums. 

The anion and the cation are frequently called the 
negative and positive ion respectively. Similarly the 
cathode and anode are termed the negative and podtiTe 
electrodes; Daniell denoted them the platinode and the 
zincode, but these terms have fallen into disuse. 

Of the bodies which are capable of electrolytic oondoc- Wbit 
tion nearly all, if not all, are liquids. Faraday (Exp. Re$., 433, Wkt 
1340) apparently obtained some chemical decOTapomtion ^^ 
in sulphuret of silver and a few other salts when solid, but^^^ 
this did not alter his opinion that the mobility secured in 
the fluid state, either by fusion or by solution, was necessary 
to the phenomena of electroljrsis ; and his view, which he 
supported by experiments on ice and other solids that 
conduct when fused {Exp. Res., 380-397, 419-428), still 
obtains. Electrolytic action doubtless sometimes takes 
place in gases, but accurate investigation of the sabjeet b 
difficult on account of the extreme mobility of 



ELECTROLYSIS 



107 



and the danger of confnaing electrolytic efifects with efifects 
dae to disruptive discharge by convection. Oases have, 
however, been decomposed by the silent discharge, as CO^ 
intoGO + 0. 

From Faraday's time attempts have continually been 
made to classify strictly, according to their chemical com- 
position or constitution, the liquids capable of electrolytic 
conduction, but hitherto without very much success. It 
most be remembered that, as the resistance of a liquid 
increases, the tests of electrolytic conduction become less 
and less sensitive. We can consider a body an electroljrte 
if we can (1) collect the products of decomposition, or (2) 
demonstrate their presence on the electrodes by means of 
the return current due to polarization. If the resistance be 
very great the former method becomes evidently very 
difficult, and in the latter complications are introduced 
which cannot here be discussed (see Electricity). On 
the other hand, we might easily be misled into consider- 
ing a body an electrolyte from the presence of mere 
traces of a foreign substance. Thus at one time water was 
regarded as the only electrolyte, but it is found that the 
purer the water is the less does it conduct electricity, and 
now Eohlrausch and Nippoldt have shown that the presence 
of one lO-millionth of H2SO4 would be sufficient to account 
for its observed conducting power, so that the weight of 
evidence goes to show that water itself is not an electrolyte 
atalL 

It is not, then, surprising that views on the question of 
what constitutes an electrolyte have changed considerably. 
Davy and the older chemists, as mentioned above, considered 
water to be the only electrolyte ; Faraday, by electrolysing 
fused chlorides, &c, dissipated these notions, but still re- 
garded water as the electrolyte which was decomposed when 
acids were subjected to the electric current, and his general 
conclusion was that an electrolyte must be a compound con- 
sisting of an equal number of chemical equivalents of its 
elements, that is, in modern notation, must be of the type 
M^^R^) where x and y are the atomicities or valencies 
of the elements whose atomic weights are represented by 
M and R, and thus that two elements would by uniting 
form only one electrolyte {Exp. Res., 679-701, 830). The 
oxygen salts for which Faraday assigned no law were in- 
cluded by Daniell in the same formula as binary compounds, 
of which the part R acting a^ anion was no longer an 
element but a compound ; thus ZnSO^ was shown to be split 
up by electrolysis into Zn and SO4 ; in that case y would 
represent the basicity of the acid forming the salt. 

This hypothesis lacks definiteness, on account of the varia- 
tion of Uie atomicity of the elements, and falls through 
altogether in the case of copper and iron, which form each two 
chlorides, (CuCl^Cu^Clj), (FeClj,Fe2Clg), both electrolytes, 
and in consequence Wiedemann {Oalv,, Bd. i. §§ 295, 346a, 
418 (5)) modifies the statement of the hypothesis, and 
considers that for a body to be an electrolyte it must be 
capable of formation by double decomposition from one of 
the simple binary electrolytes, the exchanging atoms or 
groups of atoms forming the ions of the new compound. 
Thus silver acetate gives, by double decomposition with 
sodium chloride, silver chloride and sodium acetate. Sodium 
acetate and silver chloride are therefore electrolytes of which 
Ag, 01, Na, C2H3O2 are the respective ions. This hypo- 
thetiB may be illustrated by a great number of instances : — 
the case of the decomposition of uranium compounds, 
as XJOOl into UO and 01, is a very good example. But 
Wiedemann's view would indicate that a body, in order to 
be an electrolyte, need but be one of a '* series of salts," 
and we then see no reason for excluding the hydrogen salts 
from the class ; thus H^O and HOI can be easily formed 
by double decomposition, yet the former is, when pure, one 
of the worst liquid conductors, while the latter as liquefied 



gas is apparently not decomposed even by 5640 cells of De 
la Rue's chloride of silver battery, but gives vibrationa 
indicating very high resistance. ^ Bleekrode has also shown 
that, of all the pure liquefied hydrogen acids, only HON is 
an electrolyte. On the other hand, liquefied NH3, which is 
not formed, so far as we are aware, by double decomposi- 
tion, is electrolysable by only a moderate battery of Bunsen's 
cells, giving a blue liquid at the cathode. Moreover, 
Buff (Ann, d. Chem. und Pharm., Bd. ex.) has electro- 
lysed molybdic and vanadic anhydrides after the manner 
M0O3 » M0O2 + O, but these bodies are not obtainable by 
double decomposition with a simple electrolyte. 

Miller (Elements Chem., i. § 282 (v) ) considers that an 
electrolyte must be a combination of a conductor and a non- 
conductor, and so the majority of electrolytes are. But 
alloys behave to a certain extent as electrolytes when fused 
(see Wied., Galv., Bd. i. § 328), and SnOl^, though consist- 
ing of a conductor and a non-conductor, is not an electro- 
lyte ; so that this classification is not exclusive. 

It would therefore appear that the condition does not lie 
in the chemical constitution of the body, but rather in its 
molecular state, and to this points the fact that two non- 
conductors, as H2O and HOI, on being mixed form a very 
good conductor. In addition to this, quantitative measure- 
ments of the resistance of electrolytes show that, in the case 
of many salt and acid solutions, there is a point of con- 
centration below saturation, for which the conductivity is a 
maximum. This would scarcely be the case if one alone 
of the bodies were the conductor. 

The liquids which do not conduct are very various, 
including, besides oils and resins and other organic bodies, 
benzine, iodide of sulphur, carbon disulphide, glacial acetic 
acid, fused boracic anhydride, antimonic oxide and oxy- 
chloride, the higher halogen salts of tin, liquid sulphurous 
anhydride, pure water, and pure halogen adds. For others 
see article Electricity, p. 51. 

In the description of the phenomena, in the typical case Fan- 
of electrolysis given above, it was stated that the amount of ^X" l«w 
chemical decomposition in any time is proportional to the ^^^\^ 
whole quantity of electricity which passes through the electro- 
liquid in that time ; this is true in all cases of electrolysis, l^-te. 
and was established by Faraday {Exp, Res,, v. 505, and ser. 
vii.). It forms part of the general law to which his name 
is attached, but we prefer to consider it separately for 
reasons that will appear when we discuss the statement of 
that law. We may put it thus : — If W he 'he mass of an 
electrolyte,^ decomposed by the passage of aqh antity E of elec- 
tricity , then, as long as the ions remain of tit same nature^ 



W-KE 



(1). 



where K is a constant dependent only on the nature of the 
electrolyte, and therefore indepaident of the nature or sise of 
the electrodes and of any secondary actions which may take 
place. 

It is evident that if we can prove the truth of this law Volta- 
for one electrolyte, with ions which do not vary with varia- nieteii. 
tions of electromotive force, we shall have a very con- 
venient means of measuring the total amount of electricity 
which passes through any circuit in a given time by in- 
troducing such an electrolyte into the circuit, and measur- 
ing the amount of decomposition in the given time. Fara- 

^ Bleekrode and I>e la Rue, Proc, Roy. Soc., zzt. p. 823. In fact, dis- 
ruptive discharge occurs by convection currents, or, if the electrodes be 
sufficiently near, by spark. Similar phenomena may be obaenred by 
immersing the poles of a Holtz machine in paraffin oiL 

* In what follows, the term electrolyte is used in its most general 
sense, to signify any liquid or mixture of liquids through which the 
current passes, and not necessarily one definite chemical compound. 
Hence the necessity for the condition that the ions shell not vary, as 
in mixed electrolytes ions for high electromotive forces are differsst 
from tliose for low (rid. inf. ). 



108 



ELECTROLYSIS 



Determi- 
nation of 
the ions. 




day demonBtrated the truth of the law in the case of dilute 
sulphuric acid by ezperimeats with vessels in which the 
products of decomposition of the dilute acid between 
platinum electrodes could be conveniently collected, either 
separately or together, and measured (Exp. Res,y 714- 
728.) Such an instrument he called a volta-electrometer, 
and subsequently a voltameter. After demonstrating that 
the amount of de- . 

composition was ir^/i 

independent of the 
size of the elec- 
trodes, he con- 
nected up two 
voltameters A and 
B, in multiple arc, 
as in the accom- 
panying diagram, 

and then passed .. , u * 

the whole current ^a«™™ ^^o^^^^g connection of voltameters. 

through a third C, and found that the amount of decom- 
position in C was equal to the sum of the amounts in A 
and B. He therefore applied the voltameter^ to measure 
quantities of electricity in other cases. 

Various forms of voltameter have been employed (see 
Wiedemann, GalvanismMS, Bd. i. § 317-319). The most 
accurate is the silver voltameter of Poggendorff, which con- 
sists of a vertical rod of silver with the lower end immersed 
in a solution of silver nitrate contained in a platinum 
vessel; the silver is connected with the positive, the 
platinum vessel with the negative pole of the battery, 
and the amount of decomposition is ascertained by weighing 
the platinum vessel with the attached silver before and after 
the experiment. Buff directly proved the truth of equation 
(I) for such an instrument by electrolysing silver nitrate 
solutions of different strengths between silver electrodes. 
The currents employed were varied for different experiments, 
and were measured by a tangent galvanometer, and the 
quantity E of electricity was deduced by observing the time 
of passage of the current. (An7i, d, Chem. u, Pkarm,, 
xciv. 15.) 

We have, then, in order to demonstrate generally the law 
expressed in equation (1), to measure the amount of the 
ions set free in any case of electrolysis, while the amount of 
electricity is measured at the same time by means of a 
voltameter included in the circuit. But the measurement 
of the amount of ions liberated is not always an easy task ; 
in the great majority of cases secondary actions (see above, 
p. 106) occur, the primary results of electrolysis are 
obscured, and in order to determine the nature and amount 
of the ions special apparatus and further investigation are 
necessary. 

Since the ions are liberated at the electrodes the products 
of secondary action will remain in the immediate neighbour- 
hood if the action be not too long continued. We may 
therefore determine the ions by collecting any gaseous pro- 
ducts, ascertaining the loss or gain in weight of the 
electrodes, and analysing the electrolyte in the immediate 
neighbourhood of the electrodes, taking care that the pro- 
ducts at the two do not mix by gravitation, by diffusion, 
or otherwise. 

For instance, if a fused chloride {e.g,, PbClg) be 
electrolysed with platinum electrodes, no chlorine will be 

^ Many corrections have to be applied to the observations with a 
water voltameter in consequence of — (1) the formation of ozone in the 
collected oxygen; (2) the formation of H,0, ; (3) the solution of the 
evolved gases in the water, varying with diflerent strengths of acid, 
and greater for oxygen than hydrogen ; (4) the re-combination of the 
oxygen and hydrogen if in contact with platinum (see Wied. (7a/v., l.cX 
A diagram and description of the water voltameter will be found in 
any of the nomeroos works on the subject. 



evolved at the anode, although Pb will be deposited at the 
cathode ; but if the liquid round the anode be analysed, for 
every 414 grammes of lead at the cathode will be found 339 
grammes of PtCl^ round the anode. Now the pladnnm 
must have been derived from the anode, which will be found 
to have lost 197 grammes in weight, consequently the 142 
grammes of CI were derived by the electrolysis from the 
PbCl2, and hence PbClj is electrolysed aa Pb + Clj. 

In order to separate the fluids at the two electrodes, 
various forms of apparatus have been employed. For fused 
electrolytes a W-shaped tube, which can be divided after 
the fluid has solidified, is sufficient; with solutions, how- 
ever, where the solvent introduces new complications the 
separation is more difficult, owing to the ^* migration of the 
ions" and other causes which will be considered below. 
Daniell and Miller {Phil. Trans,, 1844) used a cylindrical 
glass vessel separated into three compartments by porous 
clay diaphragms, the two end compartments containing the 
electrodes, and having tubes for conducting away gaseous 
products; while Hittorf, in a classical series of experiments 
{Pogg, Ann. J Ixxxix. xcviii. ciii. cvi.), used a number of 
bell-shaped glass vessels fitted to each other with india- 
rubber washers, the electrodes being inserted in the bottom 
and top vessels respectively. The lower end of each bell 
was covered with membrane to prevent mixing of the pro- 
ducts; the whole apparatus was filled with the electrolyte 
to be decomposed; and the products at the two electrodes 
were known to be separated if the composition of the fluid 
in one of the intermediate bells remained the same through- 
out the experiment. 

Qreat numbers of experiments have been made by dififer- 
ent experimenters in one or other of the ways mentioned, 
and they have thus proved that, whatever the electrodes, 
and whatever the electromotive force, the secondary action 
at the electrodes has no efl'ect upon the amount of diemical 
decomposition,^ and therefore the law of equation (1) always 
holds. 

We can give here but a few examples of secondary Sseoiri- 
action. A very good account will be found in Wiedemann, "7 •»■ 
Bd. i. § 326-385, with, however, the drawback of the use *^~ 
of an obsolete chemical notation. 

(1.) The ions themselves are set free, but separate into compomtU 
parts. That this is the case with oxygen salts, which are separated 
into the metal and a complex anion which is resolved into oxygen 
and an anhydride, was pointed out by DauicU {Phil. Trans. ^ 1889)» 
who gave to the SO^, derived as electro-negative ion from snlphatei^ 
the name of oxysulphion, and so on. Many similar cases oocnr in 
electrolvses of or/;anic compounds. Thus potassium acetate is dee- 
trolysed originally as KCsHjO, » R + CsH,OL ; but the anion splits 
up (partly at least) thus : 2CjHjO, - C.Hg + 2C0^ All the potassinm 
salts of tne fatty acids behave similarly, so that this becomes a gene- 
ral method of preparing the normal paraffins. 

(2.) The ions appear in an abnormal molecular date. The depoett 
of copper in Gladstone and Tribe's ZnCu couplejs a black ciystailine 
powder (see p. 114). The most important instance, however, is the 
formation or ozone in the oxygen liberated at the anode by the 
electrolysis of acid solutions, which was recognized by Sebonbein in 
1840, although the smell and powerful oxidizing properties of the . 
efij& evolved had previously been noticed by Franklin and Van lianim. 
The amount of ozone, though very small, may be recognized bv all 
the ordinary tests (KI, indigo, &c.) ; it diminishes wiUi rise of the 
temperature at which the electrolysis takes place, and ie above 8 per 
cent, when the electrolyte dilute H^O^ is cooled by ice and nit, 
and the electrodes are platinum-iridium wires (S<Mnet). With dilute 
HjSO^ at 6** C, 100 c.c. of oxygen contained '00009 gnunme osone^ 
and '00027 gramme at a mean temperature of — 9* C. ; dilute 'RfitO^ 
gave at 0* C. '00052 gramme per 100 c.c. of oxygen (Soret). The 
amount varies with the different acids, solutions of chromie tnd 
permanganic acids giving the largest percentage. 

These points are of importance in correcting obeervataons bj t^ 
water voltameter. 



' Of course, if the products of decomposition be allowed to 
late nntil the electrode is surrounded with an envelope of limiiddiftr* 
ing from the original electrolyte, the whole character of the mt owxiMJ 
tion changes. 



ELECTROLYSIS 



109 



Tha molecular state of the deposit varies very much with the 
density of the current, ue., the current strength per unit area of elec- 
trode (Bunsen, Pogg. Ann., zci. 619). With small current density 
the metals are deposited as well-shaped crystals ; on increasing the 
density, reguline metal (similar to the metal when smelted) is 
obtained, but with great density the deposit is amorphous, botry- 
oidal, or pulverulent. With some metals, the molecular state differs 
with the solutions from which they are deposited. Thus silver from 
dilate solution of the nitrate, with great current density, appears as 
a black powder, becoming grey- white and crystalline when the cur- 
rent ceases (Wied., Cfalv., Bd. 1. § 836a) but from solution of potas- 
dnm silver cyanide it is electrolysed as reguline metal. Gold and 
platinum exhibit a similar behaviour. For a good instance of 
amorphous deposit, see the account of Gore's explosive antimony 
in his EUctroTnetallurgy, p. 103. 

(8.) The ions very frequenllif read up<m the electrodes and produce 
in some cases very interesting chemical actions. If the cation and 
cathode are both metals, an alloy of the two is the usual if not 
universal result This is well known in the case of the electrolysis 
of many metals and salts with mercury electrodes, and the combina- 
tion of the hydrogen set free by electrolysis with electrodes of pal- 
ladium, nickel, and iron may be similarly regarded ; and perhaps the 
compounds derived when ammonium salts are decomposed with a 
mercury cathode. Copper, when deposited ^n platmum, alloys 
with it to a certain extent, the alloy penetratmg to a considerable 
depth (Gore, Electro-metallurgy, p. 47). Faraday noticed the com- 
bination of tin and lead with platinum electrodes in the electrolysis 
of the fused salts of those metals. 

The action of the anion upon the anode furnished Faraday with 
an accurate and convenient means of estimating the amount of 
chemical decomposition produced by a definite quantity of elec- 
tricity, and thereby oT confirming tne law given oy equation (1) 
(Exp, Res., 807-822). Thus by varying the anodes, while the cathode 
remained the same, in the decomposition of acidulated water he 
found the amount of hydro|^n liberated at the cathode, and there- 
fore the chemical decomposition, independent of the nature of the 
electrodes ; and by electrolysing various chlorides, as of silver, tin, 
lead, with an anode of the same metals respectively, he was enabled 
to determine very accurately the amount of chlorine separated. We 
shall have more to say on the bearing of this hereafter. The 
oxygen liberated by the electrolysis of acidulated water frequently 
unites with the anode; even if this is of carbon it becomes 
oxidized to CO and CO,; this was noticed by Faraday {Ecp. Res., 
744), and is interesting as showing the active state of the oxygen 
when separated, 
tro- But perhaps the most interesting examples of the action of the 
lary ions on the electrodes ai-e furnished by the capillary phenomena 
lO- exhibited by mercury in contact with dilute acid, on the passage 
k of the current If we have a drop of water upon a surface of Hg, 
and the water be connected with tne positive, while the Hff is con- 
nected with the negative pole of a battery, the water wiu gather 
itself up into a spherical drop, and on reversing the current will 
spread itself over the metal. Tnis phenomenon is supposed by Wiede- 
mann to be due, in the fonner case, to the reduction of a film of 
oxide on the surface of the Hg by the liberated H, thereby giving a 
cleaner surface with a higher capillary constant, and, in the latter, 
to the oxidation of the surface by the liberated oxygen, and this 
view is borne out by numerous experiments. Thus a reducing 
agent, such as crystal of sodium thio-sulphate (Na,S,0)), intro- 
duced into the drop of water produces similar contraction of the 
drop, while an oxidizing agent, as K.CrjO;, produces on the con- 
tra^ a similar dispersion. A drop of Hg in dfilute sulphuric acid, 
connected with the positive pole of a ^ttery, while the negative 
electrode is near it, extends toward that electrode on the passage of 
the current, becoming covered with a film of suboxide, wiiich then 
dissolves in the H^O^, and leaves again a bright surface, when the 
drop returns to its original position, and a senes of oscillations are 
thus set up (see Wied. Oalv., i. 868 sqq.). With solutions of alka- 
line cyanides containing mercury Gore obtained oscillations pro- 
ducing sounds {Blee.'Afetall., p. 197 ; Proc. Roy. Soc, 1862). It 
was observed by Erman that a drop of mercury in a horizontal 
tube, with dilute acid on both sides, moved at the passage of the 
elecbic current through the tube towards the negative electrode. 
These phenomena have been investigated further by Lippmann 
IPbgg. Ann., cxlix. 647, trans, in PhU. Mag. [4] xlvil 281). 
One of the forms of his apparatus is as follows. A glass tube A, 
drawn out to a short capillary point of about ^^^ mm. radius, con- 
tains mercury which penetrates into the fine point and partly fills 
it, the remainder being filled with dilute HsS04, into which the 
capillary opening dips; below the electrolyte is a surface of mercury, 
■erving as the positive electrode, sufficiently broad for the capillary 
tffeots there to be neglected. The negative electrode is the mercury 
in the tube A. Lippmann showed by this apparatus that, in order 
to compensate the cnange in the capillary constant of the meroury 
produced by a definite electromotive force of polarization, a definite 
inerease of pressure on the meroury in A b required. As for an 
•leetromotive force of polarization equivalent to a Daniell cell the 



compensating pressure was 260 mm., and as the quantity of elec- 
tricity required to polarize the electrodes is very small, this apparatus, 
when once it has been graduated by observing the- compensating 
pressure for known electromotive forces, may evidently be employed 
as a sensitive' and convenient electrometer for electromotive forces 
less than the maximum of polarization of the electrodes. 

We may mention one other exan;^ple of the action of the ions Passiv- 
upon the electrodes. An iron wire is usually attacked by dilute ity. 
HNOs (sp. gr. 1 '3) ; but if previously to its being immersed in that 
liquid it is employed as the anode in the electrolysis of diluted 
oxygen acids, the nitric acid has no longer any effect upon it, not 
even tarnishing the surface, and the wire differs from ordinary iron 
in being strongly electro-negative to it, and indeed to copper, in 
dilute acids (Martens, Pogg. Ann., IxL 121). It is then saia to be 
in the passive state, and is considered to be covered with a film of 
oxide which is strongly electro-negative, and insoluble in dilute 
nitric scid (Faraday, Phil. Mag., ix. p. 60, 1836, x. p. 176, 1837; 
Beetz, Pogg. Ann., Ixii. 234, Ixiii. 415). De Regnon, however 
{Comptes Rendus, Ixxix. 299), attributes tne phenomena to polariza- 
tion. This peculiar state may be induced by various processes; 
Eeir {Phil. Trans., 1790) observed it when an iron wire was dipped 
into strong nitric acid (sp. gr. 1 '5), by which its surface is not 
attacked. A more dilute solution has the same effect (Schonbein, 
Pogg. Ann., xxxviii. 444), if the wire be immersed several times, or 
if the solution contain chromic or sulphuric and permanganic acids 
(Boutmy and Chateau, Cosmos, xix. 117). Iron when dipped in 
very strong solution of AgNOs does not precipitate the silver, and 
is electro-negative even to that metal. Another method of render- 
ing iron passive, evidently the same in principle as the one first 
mentioned, is to touch the iron wire immersed in dilute nitric 
acid, by carbon, platinum, or other electro-negative element itself 
in contact with the liquid; and on the contrary, passive iron 
becomes active if it be touched by a body electro-positive to it, as 
copper or zinc. If a passive wire be partly immersed in the dilute 
acid, and an active wire in contact with it be slowly introduced 
into the liquid, the latter becomes pasidVe too ; but if they touch 
under the surface, both are rendered active. Iron is rendered 
passive also by heating in a current of oxygen or an oxidizincr 
name until it is tarnished On the other hand, the passive metiu 
becomes active under the influence of any reducing action upon its 
surface, whether by deposition of H upon it by electrolysis, by heat- 
ing the metal in a reducing flame, or by abrading the surface. One 
modification of the electrolytic method is to touch the metal in dilute 
nitric acid, for a moment, with a copper wire. The point touched 
becomes immediately active, and tnerefore electro-positive to the 
rest, and so currents are set up from active to passive metal through 
the acid, which accordingly reverse the state of both parts, and a 
curious series of oscillations result, ending in Uie whole becoming 
active. (Schonbein, I.e. Compare these with the phenomena of 
alternation of passive and active states of iron, and oT the oxidized 
and bright surfaces of amalgamated zinc described by Joule, Phii. 
Mag., 1844, i. 106). 

Iron is not the only metal which behaves thus. Nickel, cobalt, 
tin, bismuth, and even copper, all exhibit similar phenomena in 
strong H NO) and as positive electrodes ; and aluminium thus treated 
is electro-negative even to passive iron (see Wiedemann, Oalv., Bd. 
i. § 639-542). 

(4.) The ions act upon the fluid surrounding the electrodes. Second- 
Actions of this kind in both fused and dissolved electrolytes nearly ary ac- 
always occur unless the ions combine with the electrodes ; thus per- Uons. 
chlorides, if such exist, are formed from the chlorides, and per- 
chlorates from chlorates at the anode (Kolbe). At the cathode the 
secondary actions are cases of reduction ; thus if solution of potassio 
iodide be electrolysed, corresponding to 1 equivalent of iodine at 
the anode, there will appear not only 1 equivalent of H, at the 
cathode, but an equivalent of KHO as well, so that the potassium 
liberated from the iodine must have acted upon the water and 
formed KHO. If ammonium chloride be electrolysed, the chlorine 
at the anode reacts upon the NH^Cl, giving free nitrogen and 
nitrogen-chloride. The electrolysis of ammonium nitrate is still 
more interesting, as NH3 and H are separated at the cathode, where 
the hydrogen reduces the nitric acid of the nitrate, and nitro^jen 
is evolved, while at the anode NO, is deposited, which forms with 
the water nitric acid and oxygen, the latter reacting upon the 
ammonia of the nitrate, again evolving nitrogen, so that that 
element appears at both poles, — at one mixed with ammonia, at 
the other with oxygen (Miller). Some of the reactions investigated 
by Kolbe and Burgoin with organic salts are very interesting, but 
more exclusively to the chemist. The oxidizing and reducing actions 
are very powerful, as the bodies probably act in the ** nascent state.'* 

Solutions of acetate and nitrate of lead, when electrolysed by 
currents of small density, deposit at the positive electrode hy- 
drated peroxide of lead as a black powder. If a polished iron 
plate be used as the anode, the deposit shows prismatic colours 
depending on the thickness, and the process has been applied in 
the arts to colour metallic toys, under the name of metallochromy. 
If a fine wire as cathode be placed vertically above the anode plate. 



110 



ELECTROLYSIS 



tii« coloon ue arranged in circles long known as Nobili's rings. 
Similar phenomena are exhibited by salts of bismuth, nickel, 
cobidt, and manganese, all of which are precipitated as peroxides, 
usually hydrated (Wernicke, Pogg, Ann., cxlL 109), upon the anode 
by the action of the oxygen liberated by the passage of electricity. 
Silrer is ^so thrown down as a black peroxide, together with some 
oxygen from a solution of sulphate and nitrate, and iron behares 
somewhat similarly in an ammoniacal solution of the protoxide in 
yacuo. 

Such secondary actions vary very conspicuously with the density 
of the current and the temperature. Bunsen {Pogg* Ann,, xcL) 
electroljTsed solution of chromic chloride, and by increasing the 
current density obtained in succession H, Crfi^ CrO,, and metallic 
Cr at the cathode ; the reason for this is evidently that with high 
current densities the supply of ions in any time is greater than 
can take part in secondary action, and hence some of the original 
ion is deposited. A rise of temperature favours chemical action, 
and promotes rapid mixture of the ions with the solution at 
the same time ; so the higher the temperature the greater is the 
current density re(|uired to isolate the ions. From concentrated 
sulphuric acid, for mstance, below 80° only H and are obtained ; 
between 80* and 90° oxygen is given on at the anode, while at 
the cathode H and S, aue to reduction of H^SO^ by hydrogen, 
appear; above 90** sulphur alone is deposited at the cathode 
(Warburg, Pogg. Ann., cxxxv. Hi). 
Mixed Instructive and important cases of secondary action occur when 

electro- the electric current is made to traverse a mixture of several solu- 
lytet. tions. Magnus {Pogg. Ann., cii. 23) determined by ex^riments 
on dilute CuSO^ solution, in an apparatus with a porous diaphragm 
of clay, colloid paper, or animal membrane, specially arranged that 
the lines of flow should be parallel, and the current density therefore 
uniform, that there was a limiting value of the density above 
which both copper and hydrogen appeared at the cathode, but 
below only copper. His results show that this density is inde- 
pendent of length of the electrolyte and material of the electrodes, 
out varies directly as the size of the electrodes. The specific 
resistance of the constituents, as well as the relative position of the 
two ions in the *' electro-chemical series'' (vid. inf.), are of great 
importance, the electro-negative metal always appearing first. 

In order to determine whether the current traversed hoth. elec- 
trolytes or only one, Hittorf (Pogg. Ann., ciii. iS), with the 
apparatus above described (p. 108), electrolysed mixed solutions of 
potassium chloride and iodide in different proportions, and avrived 
at the important conclusion that for aU densities the current 
traversed both electrolytes, as it were in multiple arc (though the 
resistance of the mixture apparently bears no definite relation to 
the resistances of its constituents except for some of the haloid 
salts); but the products liberated depend on the secondary action 
at the electrode, and hence on the current density. The formation 
of an envelope of liquid of altered composition would also intro- 
duce complications (Smee, Phil. Mag., xxv. 437). Buff, by experi- 
menting on solution of HCl, with a small amount of H. SO4, sub- 
stantially confirms Hittorf 's results (Ann. d. Chem. u. Pharm., cv. 
156). 

These considerations are, of course, especially useful in effecting 
the deposition of alloys by electrolysis. The possibility of so doing 
appears to depend upon the composition of tne solution employed. 
An acid solution or On and Zn deposits only copper, but the 
addition of potassium cyanide determines the deposition of brass. 
Gore (EUctro-metaZlurgy, p. 61) points out that, in order to deposit 
an alloy of two metals, there must be no electric separation when the 
two metals are in contact with the liquid ; if indeed such were the 
case, a deposit of the two metals, say of Cu and Zn, would im- 
mediately act as a CuZn couple (see p. 114), and the electro-nega- 
tive metal alone would be deposited at the expense of the electro- 
positive. 
Migra- Although the amount of a salt decomposed by the passage of a 
tion of given quantity of electricity is the same whether the salt be fused 
the ions, or dissolved in alcohol, water, or other solvent, yet the presence of 
the solvent produces an important effect upon the electrolyte, which 
should not be lost sight of in quantitative experiments. The phe- 
nomenon is known as the ''migration of the ions" (HittorOi or the 
"unequal transfer of the ions" (Miller). Suppose, for example, 
we electrolyse a solution of CUSO4 containing *16 gramme of salt 
per cubic centimetre, in a vessel separated by a porous diaphragm 
into two portions A and B. Let electricity be passed through the 
solution between platinum electrodes from B to A, until 1*59 
grammes of CUSO4 have been decomposed. Then — 

(1.) 1*69 g. of CUSO4 has been removed from the solution ; 
(2.) '63 g. of Cu has been deposited on the platinum cathode ; 
(3.) *16 g. of has been evolved at the anode, and 

'80 g. of SO, absorbed there by the water of the solution. 

Now, had the electrolyte been a single fused compound, no com- 
plication could have arisen ; the liquid remaining must still have 
Deen homogeneous (except for the presence of the ions near one or 
other electrode). Bat when the salt is dissolved, it is important to 



consider /nrni whoitpart of the dolutUm the aaU hat been 

Suppose that of the CUSO4 decomposed -— th was taken from tha 

» — 1 

vessel B, and therefore ths from A. The result of electrolyiii 

n 

may then be exhibited thus (assuming that no diOfuron takes place 

through the diaphragm) : — 





In A. 


I&B. 


Before Electrolytls 
After „ } 


X g. CIXSO4. 

(x-^^1-59 g.CuS04+ 

•63 g. Cn, Indnding 
Ca deposited. ^ 


yg.CQS04. 

(f-i.l«»)g. C1IS04-I- 

-M g. ^4, indndliif 
oxygen collected. 



If the volumes of the two vessels are equal, x and ff are of 
equal, since the fluid is originally homogeneous. 

Hence A will gain "r"'63 g. Cu, and lose -— — 96 g. SO4. 

1 n-l 

B will lose —'68 g. Cu, and gain -;j— M g. SO4. 

We may therefore state the result thus : — For every equivalent 
of copper deposited upon the cathode the entire gain of copper is 

the vessel A is — th equivalent, and the entire gain of SO4 in B is 

n-l 

— — equiv. The experiment shows that the entire gain of copper 

in A is '276x'63g., andthegainofS04inBi8*724x*96g.; and 

1 
hence, for solutions of CUSO4 of that strength,— -=*276, and con* 

w-1 
sequently — - = '724, so that, of the CUSO4 decomposed, 72*4 per 

cent, is taken from A, and 27 '6 per cent from B, and the aolntion 
round the cathode is weakened much faster than that round the 
anode. This wiU be observable by the depth of the blue colour of 
the solution. If the anode be of copper aitd be vertically above the 
cathode, the effect is well seen ; for although the total amount of 
CUSO4 in solution remains constant, the difference of colour at the 
two electrodes is very apparent, and, if the action be continued, 
strong dark-blue solution drops down in thin streams from tiie 
anode through the more dilute (Magnus). 

The value of n differs for different salts, and usually for eolntioBi 
of the same salt of different strengths, though in some cases, as 
K^04, KNOs, NaCl, and KCl, the variations for great difference of 
concentration are very slight The following table shows a few of 
the results obtained by Hittorf, with the apparatus described 
above, by which errors due to diffusion were avoided. The nnmbcn 

ft— 1 
in the third column indicate what is called above 'zr't i-^t the total 

excess in e(}uivalents of the anion in the vessel containing the anodes 
corresponding to a decomposition of one equivalent m salt; or, 
except in the last few cases, that part of itie salt decomposed which 
is taken from the vessel containing the cathode. 



Salt. 


No. of cc. 

of solrent 

containing one 

gramme of salt 


n 

• 


HCl 


2-9 

86a 

140-9 

2125-9 

8-6 

18-3 

118 

412 8 

207 

25-26 

4-2 

116-7 

11 

872 

0-5 


1 

•819 
168 
•171 
•310 
•178 

•loa 

•MO 
•496 
•684 

•600 
114 

•6I» 
2-lOfl 
1-818 
2-18 


HCl 


Ha 


Ha 


HBr 


HIO, 

K9SOA 


KjSO* 


NaCl 


Fe«Clm 


*^^'o • • 

Cdlj 4 

Cdlj In alcohol .... 4 
Znl] In alcohol 



The iodides of zinc and cadmium are anomalous, but it may bf 
supposed that they are decomposed as double salts t^us : — 

2CdI,-Cd+ (Cdlj-fl,) , 
or 

8CdI,=Cd+ (2CdI,+I,). 

The total increase in the amount of an ion in one part of a T8 8B el Eleeath 
divided by a porous partition is also affected bv a mechanical ^ectiaa 
transference of the electrolyte through the pores of the diajduagm, ixr eados 
generally in the positive direction of the current, which is rerj jgum, 
noticeable in cases of electrolytes of high resistance. This wu di»» 
covered by Reuss in 1807, and observed by Ponet aoon after* 



ELECTKOLYSIS 



lU 



irards; it has been inrestigated by Wiedemann (Pogg, Ann,, 
IxzxTiL 821), and Quincke {Pogg. Ann., cxiiL 513). The fonner 
worked with a porous cell, and estimated the effect either by the 
quantity of the electrolyte which passed through the wall of the 
eeil, the pressure remainmg constant, or by the rise of pressure in 
the porous ceil measured by a mercury manometer. A current of 
moderate intensity through distilled water caused 17*77 g. of the 
electrolyte to pass through the diaphragm towards the cathode in 
a quarter of an hour, and with a 19 per cent, solution of CUSO4, a 
pressure of 176*5 mm. was observed in the cell containing the 
cathode, due to the current of a battery of Danell's cells. Quincke, 
however, employed, instead of a porous cell, a capillary tube without 
diaphragm, open at one end, and connected with a reservoir at the 
other containing one electrode, while the other electrode consisted 
of one of several pieces of platinum wire, sealed into the tube in 
various positions. His current was obtained from either a Ley den 
battery or 40 to 80 Grove's cells. The two wavs of experimenting 
gave concordant results, and showed that tlie pressure on the 
cathode vessel varies as the electromotive force between the elec- 
trodes, and so diminishes with the resistance if the current be kept 
constant. It is also, in Quincke*s apparata^ inversely proportional 
to the square of the diameter of the tube, and, for tubes of the same 
sectional area, is greatly increased by increasing the perimeter. The 
direction of motion is, as stated above, usually towams the cathode, 
and is immediately reversed on a reversal of the current, and stops 
when the circuit is broken. The rate of transfer is increased by coat- 
ing the tube with shellac ; it is different for different fluids, and 
with certain specimens of absolute alcohol, and with turpentine oil, 
the direction is reversed, unless in the latter case the tuoe is coated 
with sulphur, when the direction is as before. 
Qof Intimately connected with these phenomena is the motion of 
a solid particles contained in fluids of high resistance. Faraday 
[et. observed the motion of silk threads in water, and Jiirgensen 
made many experiments on the subject with a capillary tube 
in the form of three sides of a rectangle with bulbs at the two 
comers which contained the electrodes; in one was a porous 
diaphragm as well. Quincke {I.e.) used a similar apparatus to this, 
as well as the one described above, and observed oy means of a 
microscope a double motion of particles of starch contained in water 
subject to the action of an electric machine. Near the sides of the 
tube the particles moved towards the negative electrode, but in the 
middle in the opposito direction ; on turning the machine more 

auickly the particles near the sides g^radually lost their velocity, and 
iien l>egan to move towards the positive electrode in common with 
those in the middle. So that it is highly probable that near the 
tides the particles are in the first instance carried along hj the 
motion of the fluid there, but on increasing the current the friction 
of the liquid in contact with the tube prevents its velocity increas- 
ing ao fast as that of the particles in the opposito direction, and 
ultimately the motion of the particles in that direction becomes 
appKorent. Similar phenomena are observed with many finely 
divided bodies suspended in water, as gold, copper, graphite, silica, 
felspar, sulphur, lycopodium, &c., as well as minute drops of liquid, 
as Cd| and oil of turpentine, and bubbles of oxygen, marsh gas, kc. 
All tnese are urged in water towards the positive electrode, but in 
oil of turpentine the direction is reversed except in the case of par- 
ticles of sulphur ; the direction is also reversed for silica in carbon 
disulphide. 

ay's ConsideriDg now our first equation W = KE established, 
^ K being, as stated, dependent only on the nature of the 
electrolyte, we proceed to examine the constant K and its 
value for different electrolytes. The primary investigation 
is due to Faraday, who found that if A and B be two 
electrolytes, and if a quantity E of electricity decomposes 
a mass X of A and Y of B, then X and Y are chemically 
equivalent^ that is, are the amounts of A and B which 
would take part in a double decomposition between them. 
According to this view we have for any electrolyte W = /icE, 
where /a is the amount of the electrolyte chemically equi- 
valent to 1 gramme of water, and c is the number of 
grammes of water decomposed by a unit of electricity, and 
is called the electrochemical equivalent of water. This 
appears to be always true, but the law as usually stated 
refers to the amounts of the ions separated. The most 
general statement which the facts allow is the following, 
known as Faraday's law : — In any electrolytic decompositiofi 
whateveTy the mass w of one at lecut {usually of each) of the 
ions, simple or complex, separated by the passage of a q^ian- 
Hty of electricity E, is chemically equivalent to the amount of 
hydrogen separated by the same quantity of electricity in a 
VkUer voltameter, and hence w — mhE, where mis the chemi- 



nt 



cal equivalent of the tony andh the electrochemical equiffolent 
of hydrogen. 

Since water contains |th its weight of hydrogen A >- Ic . 

Faraday admitted as electrolytes only bodies containing 
an equal number of equivalento of their components, and 
accordingly found that the amount of either ion was equi- 
valent to the hydrogen evolved in a voltameter incladed in 
the circuit The seventh series of Experimental Researches 
was devoted to proving this most important law. Two 
methods were adopted — (1) by collecting and measuring 
the products of decomposition, a voltameter being included 
in the circuit, and (2) by introducing an anode with which 
the anion could combine (as for instance a Pb anode in 
fused PbClj) a silver one in fused AgCl), and determining 
the loss in weight of the anode. By these means the law 
was proved for simple fused electrolytes, such as the 
chlorides, ko. Daniell extended it to oxygen salt solu- 
tions, and showed that they were decomposed into a metal 
and a complex ion, this last splitting up into oxygen and 
an anhydride which united with water to form the oorre- 
sponding acid, e.g., 

ZnS04=Zn-i- (S0,+ 0). 

Matteucci and E. Becquerel added a large amount of evi- 
dence in defence of the law, which was demonstrated with 
great accuracy (to \ per cent) by Soret {Ann, de Chitn, et 
de Phys,, [3] xliL 257) for a series of copper salts; and 
by Btiff for great variations of current strength with silver 
compounds. 

So long OS we confine ourselves to normal salts there is 
little difficulty about the stetement of the relation ; even 
with such compounds as the series of phosphates, the double 
cyanides, &c., which are decomposed as in the following 
table, the amount of either ion may be considered equi- 
valent to the H of the voltameter. 



Electrolyte. 


Anion corresponding 
to H in volumeter. 


Cation. 


OtMerrer. 


Solution of 


NAiPOi 


P,0. » 

2 ^2 
P,0.^ } 

(P^.+n,o^+o.. 

H,CNH4),P,0r 1 
2 ' 9 

AgCj+Cy. « 
4(A1,8S04)+^ +1^ 


Na. 
Na. 
Na. 
Na. 

Na. 

K. 

K. 

K. 


mttorf. 

Daniell and Mm«, 
► Pkii. Tratu,, _ 
1644, p. 1 

) 

Hittorf. 


NaPOj 


NtaP.O? 


*'"4' t^7 

NajUPO* 

NaHNH4P04... 
KjFcCy. 


KAirCy* 


•-"•^'rfj ••••••••• 

K,A1,4(S04) 

\ 



Faraday's law is nearly always true for hoth ions, but there are, as Beqaerel's 
before stated, examples of elements forming two series of electroly- modifl- 
sable salts, especially when dissolved in water. In these cases the Uon. 
electronegative ion is osually equivalent to the H of the voltameter, 
or we may consider that the chemical equivalent of the positive ion 
varies, while that of the negative ion remains unchangea in the dif- 
ferent combinations ; so that ferric chloride may be regarded as a 
dichloride with fonnula feCl,, where fe=IFe; cuprous chloride 
cuCly where cu— 2Cu, and so on. Considerable confusion, too, 
arose from the arbitrary numbers for chemical equivalents which 
formerly obtained, and which caused such compounds as Al^Cl^, 
SbCl^ AuCl„ to appear anomalous, and warranted £. Becquerel 
{Ann. de Chim. et de Phys. [3] t xi. 5. 178) in considering that 
generally the amount of dectro-iugative ion alone was equivalent to 
the H of the voltameter.' This was borne out by his electrolysis 
of 2N,04, 7PbO, 3H,0, and N.O^, 2PbO, H.O, which gave J and i 
an equivalent of Pb at the cathode respectively ; but the Uw as thus 
modified faUs in the case of K,Cr,Oy, which gives K + (CrO,+iO) 
both in the melted and dissolved state, and in that of Na^^ which 
gives Na+ (S, + iS), and also for basic acetate of lead. 

* This oxygen b set free. 

' The well-known deposit of silver in electro-plating is duo to second, 
ary action of the K. 

* The chemical equivalents of Al, Sb, An wen taken to be 18*5» 61 
98 itspecUvely, instead of 91, 40*6, 65*5 as now. 



112 



ELECTEOLYSI 



Bectro- FaradAj'a law receives striiuiig conllrmatioc from the electxo- 
Ijriaa ly^B of several solutioni nmnged in aericB in contact with each 
■olationi otber bj meani either of porous septa, asbestos wicks, or aiphoc 
in eon- tuba. Each liquid then acta as an electrode to the adiacent onaa, 
tact '"^ '0 at tbe junction we have aemrated the anion of one electro- 
lyte and tbe cation of the next. These in general unite, and if the 
resulting compound be inaoluble, a precipitate is thrown down, 
Faraday thua precipitated magnesia from its sulphate by electrolys- 
ing a solution of that salt in contact with water, the current passing 
fiom the salt solution to the water. Now, in all cases in which tbe 
ions unit« at the junction, and do not appear free at all, the amonnt 
of the cation of one liquid must be chemicallj equivalent to that of 
the anion of the succeeding one, and hence obey Faraday's law. 
Many of the decompoaitiona and combinationa thus effected are 
very intfreating, a list sbowins in a tabulated form the results of 
eiperiments by Hiainger and Berzelius, Davy. Daniell, Miller, and 
others will be found in Wiedemann {Galv., Bd. i. § 368). We can 
only mention one example which is of theoretical importance. If 
the positive electrode be in solution of iodic acid which is in contact 
with diluta sulphuric acid containing the cathode, then at tbe sur- 
face of sepoiation there will be formed I and SOj, or H and SO,, 
according ss the I observed at the negative electrode in the elec- 
trolysis of HIO, solution is an ion or dne to secondary action. By 
the union of tbe two ions at the junctioD the titter is shown to be 
the case; therefore iodic acid is electralysad as H,-i-(l,Op-i-0). 
IleclTO- We gather at once from the truth of Faraday's law that we can 
chemical oaigii to each ion an electrochemical equivalent (which may be 
eqnlva- referred to as E.C.E.), which will ensble ta to dotormine at once 
lants. the amount of the ion which will be separated by a given quantity 
of electricity. With the notation already ased the E.C.L. of an 
ion =i mt. Tbe value of t— the amount of water decomposed 
by one C.G.S. electromagnetic unit of electricity — from ciperi- 
menta of Weber, Joule, Bunsen, Casselmann, and Kohlrausch is 
■00093 gramme (Wied. Oah., Bd. iiL j 1077-1078). The quantity 
m is one of the chemical equivalents of the ion, usually that de- 
duced from its most stable salts ; aome metals, indeed, with two 
series of salts have two £.C. E. s. Tbe following table of the elements 
gives the values of m and the E.C.Ka in ateolute units, as far as 
they have been eiperimentally determined. Since in bears a simple 
ratio to the atomic weight, its valne can be corrected by the reaulta 
of chenucal analysis. 







Tailoqf 


EUOnKhm 


ical£ 


^ 


•Bto. 






^ 


"SaS 


% 1 






s 






1 


-i 


y -■ 




1 


.§ 


= . 


1 


J 




s;-f 


1 


1 


si" 

a 


3^^ 
^1 


Al 


~st7 


BICl 


■mm 


Mo.... 


~M~ 


Cl 


,., 






40'S|I) 


•miw 






»'S(I) 








«;(") 




HbZ'. 




(^ 












N 




(•) 




W_.. 




wim 








11 
















aci 








eo(>) 








O 








MCl 








' 






m 


IW) 




pi'"" 




«'»![) 








K 


■O0J08 














m 










. 






(•) 








sni'i 


■00ST8 




us 


SSK') 


■w^ 






a 




cr": 






■eoisi 


St.'.'.'. 






00... 




»■«!) 




SI 


88 


c> 




C«.. 




f J|-«l) 


«MJ } 


A«.... 




lW(i) 






]«(>) 




N»... 




ra(i) 


■OMST 




M 


(■) 












F.Z'. 












leC) 




o._. 




(•) 




Tk'.'.'.'. 




p 




An-. 


1»« 


«■»(•) 


■OOWT 


Te... 






■Mats 


B..- 




(•l 




Th'!!! 


m 


tOil'l 




r._. 


IM 


"j.';> 


■oi»n 




119 


{& 


■OMlo' 






IB,.,0 


-oww 






('/ 




La... 




(•> 








l") 








1M-6(I) 








(') 
















(') 






H> 


li('KS} 






ss 


sfw'im 




Md.. 












n 




Hg.. 


»00 


& 


= f 











Every com{dei ion hat also a definite electrocheraical equivalent, 
lunaUy coinciding with ita chemical equivalent The E.C.E. of 
an electrolyte is the sum of tIie.E.G.E.B of ita component ions. 

■ FsndiJ, Sxp. Ra,, ler. vU. 

* BeniDlt (I.<^ infra]. 

• Eiltaet iliue eLenitnti biTt not been obtained ai Inu br electrolTtle atUon, 
or qaantatlTa eiperloisnM an wantlBf . 



Eennnlt* determined the E.CE.s by an iEverse method. He 
observed the amoant of the metal which, forming the negative pole 
of a battery with various electrolytes, gave a current equivalent to 
that produced by tbe dissolution of a deiinite amonnt of zinc in a 
ZnPt cell, the two currents passing through a dilferential galvano- 
meter, and thua compared the amounts of elements which generate 
tbe same quantity of electricity in combining. It is perha^ necea- 
sary to observe that the electrolytic reactions taking ^lace in a gal- 
vanic cell which genetatea a current are in every way identical with 
those dae to a current from an eitemal aouree sent throDgh the 
electrolyte. In tbe former case, the energy of chemical affinity at 
tbe electrodes is transformed into the energy of electrical separa- 
tion, and in the hitter the converse ia the case. 

Tlu Electrochemiad Seria. 

It ia evident from all the eiamples we bare given that it ia El 
not an accident whether an ion will appear at the anode or cathode ; ci 
the cations have been all more or less similar in character, and SH 
were eithft metals or more allied to the metals than the corre- 
sponding anions, which were bodies like C\, Br, 1, CN, 0, Ac. 
Faraday (^i^.^., 647) was accordingly led to consider that an 
element or radicle was unalterably either an anion or a cation ; 
thh, however, was contradicted by the fact that the same element 
may act as an anion in one solution and a cation in another, as 
19 tne case with iodine, which in Kl is an anion, but from a solation 
of iodine bromide (IBr) appears at the cathode. The electrolysis 
of alloys' points in the same direction, bo that the conclusion ii 
suggested to us that "anion" and "cation" have only relative 
meanings, and that we might arrange the elements in a series such 
tlmt, in a compound of an element A with any one of those 
above it, A would appear aa a cation, but in a compound with 
any of those below, aa an anion. To do this by parely electro* 
lytic meaus is out of the question, as binary electrolytes do 
not exist for each pair of elements. Aa far, however, as the 
series can be thus made out, it is found that, as a rule, if two 
elements A and B, such tliat A is above B in the aeries, be 
immersed in a eimple electrolyte, as dilute H^SO,, and connected 
by means of a wire, the ourrsnt flows from Bio A through the liquid. 
Hence in unknown cases we may observe the direction of the cur- 
rent when tlie two elements are immersed in an electrolvte, say 
H,80,, and determine tbe relative position in the aeriea.' With 
the series thua roughly formed, it is observed that the wider two 
elements are apart the greater is the chemical affiniW between the 
two, and thus that if we have a componnd MS, where M is the 
electro-positive element, a more electro- positive element M' having 
a greater alhnity for R than M tends to replace M from the com- 
pound, and a more electro-negative element B' tends to replace R 
aa iron replaces copper from CuSO,, and chlorine iodine from EI. 
This furtlier aaaiata us in forming an eloctrocbemical series of the 
elements, bnt it ia still not very strictly arranged, and many of the 
members of the series are placed by tbett analogy to elements whose 
positions are known. Moreover, it ia supposed that the relative 
position of two elements may vary with the temperature. Thua 
carbon which is used in batteries as the negative element, is at a full 
red heat electro-positive even to potassinm, or at least reduces 
the carbonate of that element. Jablocbkoff {Campla Stndui, Dec. 
3, 1877) describes a cell of which the positive element is coke. The 
electrolyte is fused sodium or potassium nitrate, and the negative 
element is a cast-iron vessel containing the fosedsalt. The current 
ia from coke to cast-iron through the nitrate, and tbe electromotive 
force 2 to 3 volts. 

Belzelios's final series stands thus : — 

Electro -negati VI 



^n%C 


Boron. 


Carbon. 




Antimony. 


Nitrogen. 
Fluonne. 


Tellurium. 


Tantalum. 


Chlorine. 


Titanium. 


Bromine. 


Silicon. 


Lodine. 


Hvdrocen. 


Phosphorus. 




Arsenic. 




Chromium. 




Vanadium. 


PUtinum. 


Molybdenum. 


Rhodium. 


Tungsten. 


Palladium. 



Merenry. 
SUver. 

Bismnlb. 
Tin. 

Lead. 
Cadminm. 
Cobalt. 
Kickel. 

Zinc. 

Manganese 
Uranium. 



Thorium. 

Zirconinm. 

Aluminium. 

Didymium. 

Lanthannm. 

Yttrinm. 

Glncinom. 

Magnodnm. 

Calciom. 

Lithiom. 

SodiniD. 

Potassium. 

Electrtr-jiocitiTe. 




U aerkais pecnlltHj 



ELECTROLYSIS 



lis 



Theory of EUdrolyiu. 
y, Anf b^pothcsu which serks to account foi the ph 

,o[ elcrtroljsu hoi m&inlj to deal with the two poiota — (1) that ths 
^ iODS ippesr only at the electrtxlns, uid (2) iimt the electricity it the 
Mime tims is conducted betneen the electrodea. From the iKbuviour 
of electroljtn in contact on the poasnge of the current we conclude 
that if we bad a nries ol cells couBietiug aiternatel; of K.C1 and 
KaCl, the mult of electrolysia might be represented thua : — 
Before electrolysis, 

KCl,NaCl,KCI,NaCl; 
after it, 

-KNaCl,KCl.NaCl.Clt. 

Vow, we may auppoie aimilar eSecta to occur if the cells were 
all identical, and farther we may consider the collection of moleculei 
in aoy electrolyte as such a series of cells in contact, and argue the 
electrolytic proceaa to be a aeriea of decom positions and recombina- 
tiooa atoDR ■ line of molecules resulting finally in the decamposition 
of molecules at the electrodes alone. The decomposition of aoj 
oxygen salt would be similar, with the exception that the one ion 
i* complex. Thai 

-ZnSOj, ZnSO„ ZgSOj + 

might represent the decomposition of zinc sulphate. This idea of 
alternate decompositions and recombioatioDS was originally sug- 
gested by GrotthuBS in 1805, who, howerer, attnliutod the separation 
U> attractions, due to the electrndes, varying inversely as the square 
of the disUnce. Faraday {Erp. Ba., 131 -S63, series It. } discusses the 
theory, and, while denying the attractions of the electrodes detendn 
the idea of decomposition and reformation, chienyagainstDela Rive 
andBiOanlt andChompri,andcansidenthatthecflect of the|iBS8ago 
of the current is due to a change of the chemical adinilies of the 
components of the electrolyte, and he points out (1343 sqq , ser. 
TiiL) that the decomposition ia rrobably jireceded bf a polarized 
state of the particles, as explained by him in his tbeory of electro- 
static induction. This is conlirmed by experiments of Tribe (Proe. 
Soy. Soe., ]87^S), who inserted ISa amsll stripsof silver in rows, 
parallel to the line joining the electrodes in dilute CuSO,. and 
observed that copper was deposited on the enda facing the anode, 
while gas was given off from the other enda; by comparing the 
amouota of the deposit he eiplored the electric field, showing that 
it was roQghly similar to the magnetic field due to a north and a 
•outh pole. 
ocfs Many investisstors bare suggested additions to Grotthuss's 
<Tj. hypothesis (see Wiedemann, i. 1S1, a,), and in particular HIttorf 
(Pom. Ann., Ixxxix.) bos eipandcd it to eiplain the migration 
of the ions in salt solutions inresligated by him. He supposes 
that the molecules are equal distances apart, and that the ions 
when separated travel with different velocities to the points of 
recombination, and consequently those points ore not the middle 
points between pairs of a4jacent molecules, ile thus considen that 

the cation travels — th of the distance between molecules while the 



a I Hence the whole ir 

combined, doe to electrolysis is — equivalent. 

In the portion containing the anode we shall have — (1) a gaio of one 
equivalent of anion set free, and 12) a loss of — equivalent of electfo- 
lyte due to the transhition ; and hence the whole increase in ths 

amonnt of knioD free and combined round the anode ia ( I I 

cqaivalent. The same results aie obtained if the second supposition 
be made. Hence then here used ia identical with thennseaabovein 
the account of the phenomenaof migration of the io 



anion tr«TeU [ 1 - 



- — jth of the distance. 
If then we suppose the ions separated at the electrodes to be 
removed, we may imagine the positions of the particles in the 
mtdivm o/'xilu^ion before and after electrolysis to be represented by 
a a'. . . . , respectively, thus lwheren = l) : — 



towardf that electrode 'rthot the distance between the particles, or 
M if (2) the particle at the positive electrode were removed, and all 
the reat ahifted ( 1 - '^ )^ po^ o' the distance between the partjcles 
towarda it If wa suppose the aolvent separated by a porona wall 
into two portions, we shall have after electrolysis in ths nortion 
containing the cathode (on the first supposition) corresponding to 
dapoaition of one equivalent of hydrogen in the voltameter — 

(1) a gain of one equivalent of cation deposited; 

(2) a loss of one eqnivalent of salt since the decoinposed mole- 

coles are tnpposed taken from there ; 

(8) a gain of — equivalent of salt due to translation. 



D' Almeida 

considered that the phenomena were due to the fact that round the 
positive electrode an envelope of free acid was formed by electrolysis, 
and that this became a second electrolyte in contact with the sslt 
solution, it is also evident that by sunpoaing the salt to be electro- 
lysed in a bydrated state, i.e. combined with > number of molecnlsa 
of water which may travel with either the onion or cation, an ex- 
planation of the phenomena may be arrived at (Burgoin, £ufJ. Soe. 
Chim. (2] ivil. Ui). Hittorf explained the lemstkable cases of 
tho iodides of zinc and cadmium by a somewhat similar assomp- 
tion ((>. tupra, p, 110). 

F. Kohlrausch {Natht. v. d. K. Oa. A. Wxss., Cbttingeu, 17 Mai Eiten- 

I 1S76, 4 April 1877] has recently pointed out a most remarkable sloa by 
relation between the migration constants and the conductivities of Kohl- 

I extremely dilute solutions containing 'leelrochemicali)/ equicaltTit rautch. 
amouTili of haloid or oxygen salts. Thus if I,, I, be the conduc- 

I tirities of such solutions ol two salts UR. tlR' containinir one 

' component M the ea 

I migration constants of the ion tl, then iL 

equation jj I ^' holds with remaikable accuracy for many salts. 
The quantities I,, I, ate called the *' speciSc molecular conductivi- 
ties'' oF the solutions, and ar« defined by the equation I-', where 
.-^ is the specific conductivity of a very dilute solution at IS* C. 
referred to mercury, and « is the ratio of the number of grammw 
of soli per unit of volume of solution to ita electrochemicaT equiva- 
lent in bydroi^n anits. The results are in accordance with the 
hypothesis that the conductivity of an electrolyte is nroportional to 
the sum of the oppositely directed velocities of the anion and 
cation; the velocity of any ion ia supposed to depend on the 
friction of the surrounding fluid, and is accordingly constant tor 
the same ion in different solutions if these are extremely dilute. 
A table of relative velocities csn be formed from the mig'atiou 
constants of Hittorf, Wiedemann, and Weisliei a multiple of 
these velocities gives numbers such thst the sum of those corres- 
ponding to two ions gives a value for the molecular conductivity 
of a solution of the compound of Ibe two ions freeing very 
closeljr with the cxpenmental determinations of KoElrans^ and 

In order to explain theconduclion of electricity during elccttolysis Hypo- 
several hypotheses have been susgesled, which involve the idea thesis of*' 
of continuity of electricity, even in the molecules. On Ibis view condoo- 
the elemenlary atoms when recombininc carry with them a certain tloiu 
quantity of clectncity, which, indeed, by Faraday's law, must be 
the some for every group of atoms constituting a chemical equiva- 
lent. Berzelius, for example, considers that when two atoms, t g., 
H and CI, unite to form HCl. electric distribution takes place 
similar to that of magnetism in a liar magnet, H being the pos[. 
tive pole, CI the negative. The hypothetical positive pole is then 
attracted by the negative electrode, and the attraction is so great at 
the electrode itself as to overcome the chemical affinity of the H 
for CI, and separation is the lesult, while the electricity of the 
electrode and of the H combine and are neutralized. The liberated 
chlorine atom tben behaves in the same way towards its next 
neighbour, and so the current of electricity is set up. 

For on orconiit ol the allied theories see Wiedemann. It., and see Hypo- 
also Clerk Maxwell s lemsiks upon the subject (Elic. itaa., vol. i. thesis ot 
§ 250 sqq.). These hypotheses neaily all involve ths idea, more Clauslus. 
or less defined, oF a statical molecule, it., a molecule at rest relatively 
to other molecules, and consisting of relatively Hxed atoms; but 
while we legard heat as the energy of molecular motion, this notion 
of a molecule cannot be sustained, and accordingly the above hypo- 
thesis can serve, as Maxwell suggests, merely to give precision to onr 
ideas. Clausius [Pogg. Ann.,eA. 338), however, has applied the kinetic 
hypothesis of the constitution of bodies to electrolysis, and from hi* 
suggestions we can form some conception of the method of proceed- 
ing in electrolytic action. lie supposes the molecules in the otdi- 
nary state to be in a state of agitation, and the atoms composing 
the molecules to be also in motion, sometimes separating, some- 
times recombining with other separated stoma, so that decompoai- 
tion and recombinations are conlinnally going on, but in no definite 
direction. The mean result is an apparent state of equilibrium. 
When, however, an electromotive force acts npon tba electrolyte, 

viii. - IS 



114 



£ L £! — £ L Ej 



sign. If, < 



no matter how small it is, it canses the atoms, when liberated as 
nsnal, to tend Id one direction, viz., along the lines of force. Hence 
the collection of the ions at the electrodes, where they will separate 
if the electromotive force be suificient to prevent them reacting and 
again recombioing,— in other words, sufticient to bear the polariZ' 
ation. This, though by no means a complete theory, is indeed 
applicable to ultimate atoms, and is the only one which admits 
decomposition for all electromotive forces. Clausius shows that the 
finite electromotive force is necessary to mairUain the urns in the 
iree slate at the electrodes. 
Quincke's One theory, which we must mention because it accounts at once for 
thtory. conduction, the migration of the ioos, and '* electric endosmose," is 
that due to Quincke (Pogg. Ann., cxiii., extended in cxliv.), who con* 
aiders the icns of each molecule charged with quantities of electri- 
city c and c'; then the force R tending to separate the ions from each 

dv dv 

other — - T- (Bf- E'eO, where B and B' are constants, and j: 

is the electromotive force per unit of length of the electrolyte, and is 

conseqnently — - ^, where i is the current intensity, q the 

tectional area of the electrolyte, and k its specific conductivity ; so 

that K "" rx (Be - B'('), and electrolysis takes place when this 

ia greater than the force of chemical affinity. This is a weak point 
of the theory, as a finite electromotive force would be required to 
produce any decomposition or polarization. 

The forces on the ions when separated, and hence their respective 
▼elocities, will.be proportional to « and k. This will account for the 
migration of the ions, for which c and c' are supposed unequal and 
of dififerent signs in all cases except Znl and Cdl, &c., for which 

is greater than unity ; for these * and c' may be ot the same 

sign. It, on the other hand, c be the amount of free electricity on 

a molecule of the electrolyte (supposed of high resistance) in contact 

dv 
with the glass, then- B^# will represent the force urging the fluid 

in the positive direction of the current, and perhaps producing 
endosmose, since c will be positive except for turpentine oil. So 
the motion of particles may be similarly explained by sui)posing » 
to be the charge on them due to contact with the fluid; this is 
negative with particles in water, and positive for all particles except 
solphurin turpentine oil. The results thus obtained will be found 
to Bgree closely with the experiments mentioned above (p. Ill) ; 
and the quantitative results also agree, since the force on a particle 

i 
equals B-rr, and therefore varies as the current density t, and 

inversely as the conductivity k. 
One An application of electrolysis, which has already proved to be of 

copper great value in chemistry, has been introduced of late years by 
couple. Gladstone and Tribe, in a paper read before the British Association 
in 1872 {Trans, of Sections, p. 75, see Proe. Hoy, Soc., vol. xx. p. 
218) they showed that although zinc alone does not decompose 
distilled^ water, yet if zinc foil be immersed in dilute solution of 
cupric sulphate, and be thereby coated with metallic copper, which 
is thrown down as a black crystalline powder, containing traces of 
zinc only if the time of immersion be very long (Journal Uliem, Soc., 
1878, p. 452), and if the zinc copper couple thus produced be 
immersed m distilled water at Ordinary temperature, about 4 cc. 
of H can be collected per hour. The hydrogen is seen hy the 
Oiicroscope to collect upon the copper crystals, while the zinc is 
oxidized, and forms a hydrate. The rate of evolution of hydrogen 
varies with the temperature ; the relation may be exhibited by a 
curve very similar to the curve of tension of water vapour. 
Gladstone and Tribe have found this a powerful method of acting 
upon many organic bodies, particularly the halogen compounds 
ot the alcohol radicles. In all cases either new reactions were set 
up, or the temperature at which reaction takes place was very much 
lower than witti ordinary zinc (see the series of ^pers by Gladstone 
and Tribe in the Jour, Chem, Soc., 1873-6). To the chemist the 
ZnCu couple affords an exceedingly convenient way of arranging 
electrolysis, since the whole may be contained in one vessel. For 
the copper in the arrangement, gold or platinum may with great 
advantage be substituted oy immersing zinc foil in solutions of the 
chlorides. 

This easily explains the well-known custom of generating hydro- 
gen from zinc and sulphuric acid, to which a little CUSO4 ^ added ; 
ind the ''local aotion' in batteries, when currents pass from one part 
h the other of the same mass of metal and consequently energy is 
expended for which no external equivalent is obtained, may be 
similarly referred to the diflerence of composition of the metals in 
the two places. It should be remembered that Davy suggested 
the preservation of the copper sheathing of ships by attaching plates 
of in; the same object is now achieved by using an alloy of the 
two metals. 

The application of the principle of the conservation of cnercy to 
electrolysis has already produced valuable results ; research, how- 



ever, in this direction is rendered difficult on account of the great 
-number of circumstances which have to be taken into account, in 
computing the balance of energy expended and work done ; the 
chemical composition and physical state of the electrolyte, the 
moleculai condition of the ions, and the secondary actions at the 
electrodes have all to be taken into account. For a notice of the 
present state of this branch ot the subject the leader is referred to 
the article ELECTRicixr. (W. N. S.) 

ELECTRO-METALLURGY, a term introduced by the 
late Mr Alfred Smee to include all processes in which elec- 
tricity is applied to the working of metals. It is far more 
appropriate than the French equivalent galvanoplastie^ or 
the German Galvanoplasttkf since the metals are certainly 
not rendered plastic under galvanic action, though it is true 
that in electrotypy, which forms one branch of electro- 
metallurgy, the metal is deposited in moulds, and can thus 
be used to reproduce works of plastic art 

It was observed as far back as the beginning of the 
present century that certain metals could be *' revived " 
from solutions of their salts on the passage of a current of 
electricity. The germ of the art of electro-metallurgy may 
undoubtedly be traced to the early experiments of 
Wollaston, Cruickshank, Brugnatelli, and Davy ; but it re- 
mained undeveloped until the late Professor Daniel! devised 
that particular form of battery which bears his name, and 
which he described in the Philosophical Transactunu for 
1836. A Daniell's ceil consists, in its usual form, of a 
copper vessel containing a saturated solution of blue vitriol 
or sulphate of copper, in which is placed a porous cylinder 
containing dilute sulphuric acid ; a rod of amalgamated 
zinc is immersed in the acid, and on the two metals being 
connected by means of a conductor, electrical action is im- 
mediately set up. The zinc, which forms the positive or 
generating element, is dissolved, with formation of sulphate 
of zinc ; whilst the blue vitriol is reduced, and its copper 
deposited, in metallic form, upon the surface of the copper 
coutaining vessel, which forms the negative or conducting 
element of the combination. Any one using this form of 
battery can hardly fail to observe that the copper which is 
thus deposited takes the exact shape of the surface on which 
it is thrown down, and indeed presents a faithful counter- 
part of even the slightest scratch or indentation* Mr De la 
Rue incidentally called attention to this fact in a paper 
published in the Philosophical Maga^ne in 1836, but it 
does not appear that any practical application was at the 
time suggested by this observation. Indeed, the earliest 
notice of electro-metallurgy as an art came from abroad 
two or three years later. 

St\iTgeoii*3 Annals 0/ Electr'icity for March 1839 contained 
a letter from Mr Guggsworth, announcing that Professor 
Jacobi, of St Petersburg, had recently discovered a means 
of producing copies of engraved copper-plates by the agency 
of electricity. This was the first news of the new art which 
appeared in England, and it evidently referred to the 
paper which Jacobi communicated to the St Petersburg 
Academy uf Scieucos on October 5, 1838, and in which he 
explained his process. In the Athenctum of May 4, 1839, 
there was a short paragraph relating to Jacobins discorery, 
and public attention in this country was thus drawn to the 
subject Only four days after the appearance of this 
paragraph, Mr Thomas Spencer, of Liverpool, gave notice 
to the local Polytechnic Society that he would read a paper 
on a similar discovery of his own. This paper was not r^ui, 
however, until September 13 ; and although the author 
wished to describe his process before the British Abso- 
ciation at Birmingham in August, it appears that bis 
communication was never brought before the meeting. 
In Mr Spencer's paper, which was eventually pnblisked by 
the Liverpool Polytechnic, he states that his attention was 
first directed to the subject by mere acoident: he had used 
a copper coin, instead of a plain' piece of copper, in a 



ELECTRO-METALLURGY 



115 



modification of Danieirs cell, and on removing the deposited 
metal he was struck with the faithful copy of the coin 
which it presented, though of course the copy was in 
intaglio instead of relief. Yet even this observation was 
allowed to remain unproductive until another accident 
called his attention to it afresh. Some varnish having 
been spilt upon the copper element of a Danieli's cell, it 
was found that no copper was thrown down upon the sur- 
face thus protected by a non-conducting medium ; hence it 
was obvious that the experimentalist had it in his power 
to direct the deposition of the metal as he pleased; and this 
led Mr Spencer to prosecute a series of experiments by 
which he was at length able to obtain exact copies of 
medals, engraved copper plates, and similar objects. It 
should be mentioned that between the date on which he 
announced his paper and the date on which it was actually 
read, Mr C. J. Jordan, a printer, described experiments 
which he had made in the preceding year very similar to 
those of Spencer. This announcement was made in a letter 
published in the London Mechanics^ Magazine for June 8, 
1839. It thus appears that three experimentalists were 
close upon the same track about the same time, but it is 
generally admitted that among these competitors Mr Spencer 
has the merit of having been the earliest to bring his 
process to perfection, and to demonstrate its practical 
value. 

Soon after the appearance of Mr Spencer's paper, it 
became a fashionable amusement to copy coins, seals, and 
medals by the new process. These copies in metal are 
termed electrotypes. The apparatus employed in the early 
days of the art, and which may still be conveniently used 
for small electrotypes, is similar in principle to a single 
Danieirs cell. It usually consists of a glazed earthenware 
jar containing a solution of sulphate of copper, which is 
kept saturated by having crystals of the salt lodged on a 
perforated shelf, so that they dip just below the surface of 
the solution. A smaller porous cylinder, containing very 
dilute sulphuric acid, in which a rod of amalgamated zinc 
is placed, stands in the jar, and is therefore surrounded by 
the solution of sulphate of copper. The object to be copied 
is attached by a copper wire to the zinc, and is immersed 
in the cupric solution. It thus forms the negative element 
of a galvanic couple, and a current of electricity passes 
from the zinc through the two liquids and the intervening 
porous partition to the object, and thence back to the zinc 
through the wire, thus completing the circuit During this 
action, the ^nc dissolves, and sulphate of zinc is formed; 
at the same time the copper solution is decomposed, and 
its copper deposited upon the metallic surface of the 
object to be coated, — the solution thus becoming weaker as 
it loses its copper, but having its strength renewed by con- 
sumption of fresh crystals of blue vitriol To avoid the 
complete incrustation of the metal or other object, one 
side of it is coated with varnish or some other protective 
medium, so that the deposition of copper takes place only 
on such parts as are exposed. The deposit may be easily 
removed when sufficiently thick, and will be found to 
present an exact counterpart of the original, every raised 
line being represented by a corresponding depression. To 
obtain a facsimile of the original it is therefore necessary 
to treat this matrix in the same way that the original was 
treated, and this second deposit will of course present the 
natural relief. Another method consists in taking a mould 
of the original ooin in fusible metal, and then depositing 
copper upon this die, so as to obtain at once a direct copy 
of the original 

Considerable extension was given to the process by a 
discoveiy, apparently trivial, which was first announced by 
Mr Murray at a meeting of the Royal Institution in 
January 1840. He found that an electro-deposit of metal 



could be formed upon almost any material if its surface 
was rendered a conductor of electricity by a thin coating of 
graphite or *' black-lead." Instead, therefore, of copying a 
coin in fusible metal, or indeed in any metallic medium, it 
is simply necessary to take a cast in plaster-of-Paris, wax, 
gutta-percha, or other convenient material, and then to coat 
the surface with finely-powdered black-lead, applied with a 
camel-hair pencil Medals in high relief, with much 
undercutting, or busts and statuettes, may be copied in 
electrotype by first taking moulds in a mixture of glue and 
treacle, which forms an elastic composition capable of 
stretching sufficiently to permit of removal from the object, 
but afterwards regaining its original shape. 

About the same time that Murray suggested the use of 
black-lead, Mr Mason made a great step in the art by 
introducing the use of a separate battery. Dani ell's cell, in 
consequence of its regular and constant action, is the 
favourite form of electric generator. The copper cylinder 
of this arrangement is connected with a plate of copper 
placed in a trough containing a solution of sulphate of 
copper, to which a small quantity of free sulphuric acid is 
commonly added ; whilst the ziuc rod of the cell is con- 
nected with the objects on which the copper is to be 
deposited, and which are also suspended in the bath of 
cupric solution. The current enters the bath at the surface 
of the copper plate, which is the anode or positive pole of 
the combination, and passes through the solution to the 
suspended medals which constitute the cathode or negative 
pole. As fast as the copper is thrown down upon these 
objects, and the solution is therefore impoverished, a fresh 
supply is obtained by solution of the copper plate ; this 
copper is consequently dissolved just as quickly as the 
electrotypes are produced, and no supply of crystals is 
needed, as in the case of the DanieU cell The great 
advantage of using a separate battery is that several objects 
may be coated at the same time, since it is only necessary 
to attach them to a metal rod in connection with the 
battery. Almost any form of galvanic arrangement may 
be employed by the metallurgist as a generator of 
electricity. But as the exciting liquid in a battery needs 
to be replenished from time to time, and as the zinc plates 
also wear out, its use is attended with more or less incon- 
venience in the workshop, and the electro-metallurgist has 
therefore turned his attention to other sources of electricity. 
Indeed, as far back as 1842, when the art was but in its 
infancy, a patent was taken out by Mr J. S. Woolwich for 
the use of a magneto-electrical apparatus ; and of late years 
powerful machines in which electricity is excited by means 
of magnetism have been introduced into electro-metallurgical 
establishments. When a bar of soft iron, surrounded by a 
coil of insulated copper wire, is rotated between the poles 
of a magnet, a current of electricity is induced in the coil 
at every magnetization and demagnetization of the core. 
By means of a commutator, these alternating currents in 
opposite directions may be converted into a constant stream 
of electricity, available for the deposition of metals by 
electrolysia The armatures are rotated by mechanical 
means, such as the use of a steam-engine, and hence the 
electricity is ultimately produced by conversion of 
mechanical work. 

In the machine constructed by Mr Wilde, which has 
been largely employed by electro-metallurgists, a small 
magneto-electric apparatus, with permanent magnet, is 
employed to excite the electromagnet of a much larger 
machine. The induced current of the second machine is 
stronger than that of the first in proportion as the electro- 
magnet is more powerful than the permanent magnet ; this 
second current may then be used to excite another electro- 
magnet, and hence by means of this principle of accumula- 
tion, currents of great energy may be obtained. The 



116 



ELECTRO-METALLURGY 



armatares in these machines are contracted on Siemens's 
principle, and consist of long bars of iron magnetized 
transversely, and having the wire wound longitudinally. 
During the rotation of the armature, so much heat is 
developed that special means are taken to prevent its 
accumulation. In another form of Wilde's machine, a 
vertical disk carrying a number of coils, each with its own 
core, is caused to rotate between two rings of magnets. A 
powerful machine, with multiple armatures of this kind, is 
used by Messrs Elkington at Birmingham, and is capable 
of depositing i^ cwt. of copper every 24 hours. 

Another recent modification of the magneto-electric 
machine used by electro-metallurgists is that invented by 
M. Gramme. A ring of soft iron carrying a large number 
of coils of insulated copper wire is caused to rotate between 
the poles of a fixed horse-shoe magnet, and the currents 
induced in the coils are collected by two metallic disks, 
whence they may be drawn off for use in electro-deposition. 
As the core is circular, the magnetization proceeds con- 
tinuously, and hence the currant is uniform ; but as both 
poles of the magnet are used, two opposite continuous 
currents are simultaneously produced. 

Thermo-electricity is another source of electromotive 
power of which the practical worker has availed himself. 
In 1843 a patent was taken out by Moses Poole for the 
use of a thermo-electric pile in place of a voltaic battery, 
but it is only within the last few years that such a source 
of electricity has been introduced into the workshop. The 
best-known form of thermopile is that devised by M. 
Clamond of Paris. One element is formed of tinned 
sheet-iron, and the other of an alloy composed of two parts 
of zinc to one of antimony. A large number of these pairs, 
insulated from each other, are arranged in circular piles 
around a central cavity, in which their junctions are heated 
by means of a Bunsen burner. The ease with which such 
an apparatus can be manipulated recommends this source 
of electricity to the electro-metallurgist. 

Having procured a supply of electricity from one or 
other of these sources, the electro-metallurgist applies it 
either to the deposition of a metal upon a matrix or to the 
coating of one metal by another. Hence the art of electro- 
metallurgy divides itself into two branches, one being called 
eiectrotypy, and the other being generally known as electro- 
plcUtng, In an electrotype the reduced metal is separated 
from the mould on which it is deposited, and forms a dis- 
tinct work of art ; whilst in electro plating the deposited 
metal forms an inseparable part of the plated object 

It has already been explained how electrotypes are 
generally taken. One of the most important branches of 
this art is that of producing copper duplicates of engravings 
on wood. A cast of the block is first taken in wax or in 
guttapercha, and when cold the surface of this mould is 
brushed over with black-lead ; by means of a wire, the 
black-leaded mould is suspended in a bath of sulphate of 
copper connected with a battery, and in the course of a 
few hours a sufficiently thick plate of copper is deposited. 
The copy, on removal from the mould, is strengthened by 
being backed with type-metal ; it is then planed smooth 
at the back, and mounted for use on a wooden block. This 
process is now carried out on a large scale, since it is found 
that a greater number of sharp impressions can be obtained 
from the electro than from the wood. For rotary printing 
machines the electrotypes are curved. Set-up type is also 
sometimes copied thus instead of being stereotyped, the 
electro-deposited copper being harder than the stereo metal 

Copper is sometimes thrown down as a thin coating upon 
plaster busts and statuettes, thus giving them the appearance 
of solid metal. In Paris, too, it is now common to give a 
thin coat of electro-deposited copper to exposed iron work, 
such as gaa-lamps, railings, and fountains. The iron is 



first painted, then black-leaded, afterwards electro-coppered, 
and finally bronzed. Cast-iron cylinders used in calico- 
printing are also coated with copper by a single-cell 
arrangement ; and it has been suggested to coat iron ships 
in a similar manner. Usually, however, the electro-plater 
has to cover the baser metals with either silver or gold. 

Eleclro-piaiing was introduced very soon after the dis- 
covery of the art of electro-metallurgy, the earliest in- 
vestigators being Messrs Q. R and H. Elkington, Mr 
Alexander Parkes, and Mr John Wright in this country, 
and M. de Ruolz in France. It was Mr Wright who fiist 
employed a solution of cyanide of silver in cyanide of 
potassium, and this is the solution still in common use. 
It should be borne in mind that the cyanide of potassium 
is a very dangerous poison. The objects to be silver-plated 
are usually made of German silver, which is an aUoy of 
copper, zinc, and nickel. Before being placed in the 
depositing vat, the articles must be thoroughly cleansed. 
Grease is removed by a hot solution of caustic potash, and 
mechanical cleaning is commonly effected by means of a 
bundle of fine brass wires, known as a '' scratch-brush /' 
the brush is mounted on a lathe, so as to revolve rapidly, 
and is kept moist with stale beer. Articles of copper, 
brass, and German silver are usually prepared by being 
dipped in different kinds of '' pickle," or baths of nitric and 
other acids. To insure perfect adhesion of the coating of 
silver, it is usual to deposit a thin film of quicksilver on the 
surface, an operation which is called ''quicking." The 
quicking liquid may be a solution of either nitrate or 
cyanide of mercury. After being quicked, the articles are 
rinsed with water, and then transferred to the silver-bath, 
where they remain until the deposit is sufiiciently thick. 
The quantity of silver must depend upon the quality of the 
article : one ounce of silver per square foot forms an 
excellent coating, but some electro-plated household goods 
are turned out so cheap that they must carry but the 
merest film of silver. The vats in which the electro-plating 
goes on were formerly made of wood, but are now usually 
of wrought iron. Plates of silver are suspended from a 
rectangular frame connected with the positive pole, whilst 
the articles to be plated are suspended by wires from a 
similar smaller frame communicating wilii the negative 
pole. Large articles are suspended from wires, looped at 
the end, and protected in tubes of glass or india-rubber, 
whilst small articles may be placed in wire cages or 
in perforated stoneware bowls. On removal from the 
depositing vat, the plated objects are usually dipped in hot 
water, then scratch-brushed with beer, again washed with 
hot water, and finally dried in hot sawdust A bright 
silver surface, requiring no further treatment when removed, 
may be obtained by adding to the silver bath a very small 
proportion of bisulphide of carbon. 

Electro-gilding is effected in much the same way as 
electro-silvering. It is found, however, that magneto- 
electricity cannot be employed with advantage. Various 
gilding solutions are in use, but preference is usually given 
to the double cyanide of gold and potassium, originally 
introduced by Messrs Elkington. The solution is generally 
used hot, its temperature ranging from 130* Fahr. to the 
boiling-point. If the object to be gilt is not of copper, it 
is usual to coat it with an electro-deposit of copper before 
submitting it to the gilding solution. The coating of gold 
is generally very thin, and only a few minutes' expoeure to 
the hot solution is necessary to effect its deposition. When 
the solution is fresh, a copper anode may be employed, 
its place being taken by a small gold electrode after the 
solution has been in work for some time. The presence of 
copper in the solution imparts a full reddish colour to the 
electro-deposit of gold ; and the tone of the metal may ako 
be modified by the presence of salts of various other 



£j L £ — £i L £j 



117 



lUBtals, mcli u those of iilver. Sometimes only part 
ot an object is to be gilt, snch ns the inside of a aiWer- 
plated cream-jug ; in this case the vessel vould be filled 
Kith the gilding solntion, in which the anode of the battery 
is immersed. Qold is sametimes deposited not as a coating 
npon other metals, but as an electrotype in gutta-percha or 
iu plaster moulds ; small objects of elaborate workmanship 
being thus produced in solid gold, without the workman- 
ship of the chaser and engraver 

Although copper, silver, and gold are the metals to which 
the attention of the electro-metallurgist is usually restricted, 
it should be remembered that be is also able to obbun 
electru- deposits of a vety large number of other metals. 
Many of these are not practically used, but one of them 
has of late years become of cousiderable importance. This 
ia the metal niciel In 1869 Dr Isaac Ai^ms of Boston, 
United States, patented a process for depositing nickel from 
■olutions of various double salts ; but Dr Gore had many 
years previously employed similar salts in England, and 
had published the results of his experiments. The depoai- 
tion of nickel, especially from the sulphate of nickel and 
ammonium, is now carried out on a large scale both in 
England and in the United States. The metal is deposited 
as a very thin but excessively hard coating, and has the 
advantage of not readily tamtshing or corroding even in a 
mobt atmosphere. Hence it has become common to electro- 
nickel iron and steel objects for use on board ship, as well 
u gun-barrels, sword-ecabbarda, harness furniture, gas- 
bnmecs, and various articles for household use. 

Iron, like nickel, may be deposited from its double 
Baits, and excellent results have been obtained by Klein, 
of St Petersburg, with the double sulphate of iron and 
ammonium. Engraved copperplates are much harder when 
faced with electro-deposited iron than when unprotected, 
and they consequently yield a much larger number of im- 
pressions before losing their aharpneaa. Plates for printing 
bank-notes have been treated in this way. 

Not only cau the electro-metallurgist deposit simple 
metals, sudi as those noticed above, but he ia able likewise 
to deposit certain atlnyi, such as brass, bronze, and Qermau 
■ilver. The processes by which this can be effected are 
not, however, very generally used. 

Among the minor applications of electro-metallurgy we 
may meotion the process of electrotyping flowers, insects, 
and other delicate natuml objects. These are first dipped 
for a moment in a warm solution of nitrate of silver in 
alcohol, and then exposed to a reducing liquid, such as a 
solution of phosphorus in bisulphide of carbon ; an electro- 
depoeit may then be thrown down upon this metallized 
surface. Daguerreotypes are sometimes improved by coat- 
ing them vrith a very delicate film of electro-deposited gold. 
Again, in same of the modem photographic processes for 
printing, copper electrotypes are taken directly or indirectly 
from the bichromatized gelatine. Of late years, too, a 
method of refining crude copper by means of electro- 
metallurgy has bean introduced, and is now successfully 
carried out on a large scale. Slabs of blister-copper are 
plunged into a solution of sulphate of copper, and form the 
anodes of a battery ; the copper then dissolves, and is de- 
posited in a condition of great purity at the opposite pole, 
most of the impurities sinking to the bottom of the 
depositing vat The process should be restricted to copper 
which is free from any metals likely to be deposited along 
with the metal under purification. 

It hu bmn considered desiral)U Dot to include withia the limits 



e the treatise* of G. Gore (1877), J. Napier (6th ed.. 1876), A. 
Witt (5th ed., 1874), A. Smee {3rd ed., ISSl), and O. Shav (18(4); 
C. v. Wklker'i EUdntypt UanipulatiiM (18E0) ; snd H. Dirck's 
Bidarji ^ Sltdn-mtUUittrn (18M). (F. W. R') 



ELECTROMETER. An electrometer, according to Sir DtOoi- 
Wm. Thomson, who is the greatest living authority on this tton of 
subject, and has done more than any one else to perfect fi^ 
this kind of physical apparatus, ia "an instrmnent for 
measuring difierences of electric potential between two con- 
ductors through the effects of elatroslatie force." A gal- 
vanometer, on the other hand, which might ahio be defined 
as an instrument for measuring differences of electric poten- 
tial, utilizes the dtctromagnetic forces due to the currents 
produced by differences of electric potential An instru- 
ment deugned merely to indicaU, without measuring, differ- 
ences of electric poteutial Is called an electrotcopt. It ia 
obvious that every electrometer may be used as an electro- 
scope, and it is abu true that all electroscopes are electro- 
meters more or less ; but the name electrometer is reserved 
for such instruments as have a scale enabling us, either 
directly or by appropriate reduction, to refer differeQceB of 
potential to some unit. 

The modem electrician Is far more concerned with 
measurements of electric potential than with roeaaurements 
of electric quantity; and consequently all modem 
electrometric instraments ore suited for direct measure- 
ments of the former kind. It is only indirectly that snch 
instruments measure electric quantity. With the older 
electricians it was otherwise ; and some of the earlieet 
electrometers were designed for the direct measurement of 
quantity. 

Such was the measuring jar of lAne,' represented in Eg. 1 (after laas's 
Riess). D is a Leydea jar, futened to • stand in inch a way that jar. 
its outsr armature caa be 
insalstad or connected to 
earth at will. The inner 
annatars is in good metallic 
connection with the knob C. 
A horizontal metal piece A 
' mounted on a glass pillar, 






BQotbsr ic 



be a 



required distance from C by 
means ol a screx and gra- 
duatioEL The piece A i) 
connected with the outer 




addeil by Riess, 
arrangement of the apparatus 
we ^ve been describing. 
One way of uaing the in- 
strument is as foUowa. The 
balls are set at a conreaieot 
distance apart, the stand is 
carefullf insulated, and the 

connected with the battery Fio. 1.— Laoei Jar. 

of jars or other system to be 

charged, and the inner annature with the source of electricity, ssy 

the prime conductor of an electric machine. The electricity accu- 
mulates on the inner armatmv till a certain ditTerence of potential 
between C and A is reached, and then a certain quantity q of elee 
tricity passes from C to A in the tonn of a spark, after which a 
ijuantity q remains distributed between tbe outer armature and the 
accamalator which is being charged. This procoas ia continued, 
and as each apark ]«ssea, a quantity g is added to the charge on the 
outer armature and accumulator, llence if the capacity of the 
outer armature be negligible compared with that of the accumu- 
lator, the charge of the latter will be proportional to the number 
ot sparks between the balls. Tlie measuring Jar may also ba used 
to mcaaura the overflow of electricity from one armature of an 
accumulator when the other is connected with an electric machine. 
In this case the ontcr coating of the jar is connected with the earth, 
and C is conn eclfd with the armature of theaccumulator. There is 
no occasion to discuss minutely liere the corrections necessary in the 
latter method of using the ap^iaratos ; on these and kindred points 



' Phil. Trim:, 1769. 

» The object ot the Bne 
and prerent the diiintegration of . . 
the action of tli« apparatus imgnlar (see Riess, KmbungteUclneitat, 
I 886). 



118 



ELECTROMETER 




ooninlt tbe iccotuit giren by Mascart, TraiU t^ElectridU Statiqut, 
lorn. i. g! 313-318, and Riess, I.e. 

The torsion balance of Coulomb is anothet instnmieDt suited for 
tbe direct measure me tit of electrical quautiCy. For iU coHBtraction 
and 038 Bee the article ECLECTRicmr, p. 18, 
OiKharg- The dischatging electrosciipe of Gaugain belongs to tbe present 
Ing else- class of inatniments. It conaUta (hg. 2) of an ordinary (old- 
troaoope. faahioned) golil-leaf electroscope, with tbe addi- 
tion of a small knob B, connected vrrlh the metal 
sole of the instrnment, and standing a little 
to one side of oae of the leaves. The cLarge on 
anj conductor is measured by connecting it with 
tbe knob A through a sufficient lenatn of wet 
cotton to retard the discharra properly." When 
a certain amount of electricity has reacbed the 
Kold leaf, U is attracted to the knob B attd is 
discharged; it then falls back, is lechat^ed, then 
discharged by contact with B d second time, and 
M on. It is found that Ibe same quanltty of 
electricity is discharged at each contact if the 
process be properly regulated ; so that the irbole pta. 2 — DischaTC- 
charse on tbe conductor is mewured by tbe ing Electroscope 
nninber of oscillations of ths gold leaf required 
to discharge it completely.' 

The rest of the instruments (save oae) to be described 
ma; be cUssiSed under the three heads given by Sir Wm. 
Tbomsoa in his valuable report on electrometers,' viz., (1) 
repulsion electrometers, (2) attracted disc electrometers, 
and (3) symmetrical electrometers. 

I. AmiZridnEferfTTmirfm.— Tbe eleclroscopicneedleof Gilbert is 
the oldeat apecimcn of a repulsion electroscope. The linen 
threads of Franklin, and the double pendulum used by Canton, 
Dn Fay, and others, which was an improvement thereon, are 
typical of another species of electroscope coming under the same 

Oarallo's Carallo's electroscope* (Gg. 3) embodies tbe double pendutam 
sleetro- principle. It consiala of 
•cope. two fine silver wires loailed 

with smalt pieces of cork 

or pith, and suspended 

inside a small glass cylin- 
der. Through tbe cap 

which closes the cylinder 

passes tbe stout wire from 

which the pendulums are 

suspended. Thiswire ends 

in a thimble-shaped dome 

A, which comes down very 

nearly to tbe cap ; the out- 
side of the cap and part of 

tbe wire are covered with 

sealing wax, and the object 

of tbe dome is to keep 

mtnsture from tbe stem, 

so that tbe electroscope 

could be lued in tbe open 

tJ'^Sj'SS',™*™: r.o. 3.-c.«n.'.Ei,t™«p.. 

neaa of tbe instrument two strips of tinfoil are pasted on tbe glass 
at B and C opposite the pith balls. An electroscope similar to this 
was used by Saussure.* Volta nsed a pair of straws instead of tbe 
pith ball pendulums. 
Bennet's ^7 ^" '*•* most' perfect form of electroscope on the double 
ItPld-lsif pendulum principle is the gotd-leaf electroscope of Bennet,* Fif(. 
dsctro- * represents a modem form of this instrument. The gold leaves 
fgmt. *•" gummed on the two aides of n flat piece of metal carried by a 
stoat stem, wbich pasnes thron^h the top of a glass shade and ends 
in a fiat disc. By means of this disc we may convert the instru- 
ment into Volta's condensing eleotroscone (already deacnlied, see 
Electbicitt, p. 31). Inside tbe ^lass shads, and rising well over 
tbe leaves, stands a cylinder of wire game, which ought to be in 
metallic connection with the earth, or with some couclnctor whose 
potential is taken as the standard of reference. The introdactien 
of tbe wire cylinder is dne to Faraday, and is an essential improve- 
ment ; iC is absolutely necessary, in fact, to convert the instrument 
into a tnistwarthy indicator of di (Terences of potential. Itwrvesthe 
doable purpose of protecting the leaves from eitemal d^rbing 
inflnences, and of ensuring that tbe instrnment always indicates the 
difference between the potential of the body connected with ths 




' Tberv Is scorrecUon (at residue, see Mascart, t. i. | 317, kc. 

* BriL Auoe. lUp. IWl, at Reprint n/ Papertm BUxtntiUUictaHt 
(aa»ttit»,%S*Z. '17771 

* Bless, i% 19 and 60. • Phd. Tram.. 1787. 



and another dtfinite potential. Tbns, if we insntete the sole 
electroscope, and connect A with the leaves, and B with the 
the divergence of the leaves corresponds to the difference 
;n tbe potentials of A and B, and will always be same for 
.me potential difference.* Hence, if tbe divergence of tbe 
were read off by means of a properly constructed scale, tbe 
might be osed as a rough electrometer. Tbe value of 



C I 




1 



Fig. i. — Banncfs Electroscope, 



The electrometer of Henley,' sometimes called Henley's qnadrant Henlty'j 
electrometer (fig. 5), may be taken as the type of single pendulum electro- 
electroscopes. It consists essentially of a pendulum A binged to metei. 
a vertical support C, which carries a vertical graduated senucircle 
B, by means of which the deviation of A from tbe vertical can be 
read oS. This form of electroscope is, or was, much need foi 
indicattng tbe state of electrification of tbe prime conductots of 
electric machines. The stem is screwed into the conductor, and 
the divergence of the pendulum indicates roughly the charge. 

The sine electrometer of August, represented io fig. 6, is a modi- Penda- 
fication of tbe single pendulum electroscope, analogous in principle I 
to Pouillet s sine compass. A is a 
pendulum suspended by two threads to 

... ~ T..„ti^r. Ir, ..... T.1-.T,^. R .*. . 1..il 









abaU 



fixed to the case, and connected with 
a suitable electrode. Any charge is 
given to A ; 1) is charged with q units 
of electricity ; the case is turned 
tbrougb an angle « in a vertiisl plane 
until the distance between A and B it 
the same as it was when botb were 
neutral; then, if tbe charge on A be 
always tbe same, 



This instrument is interesting or 
count of the principle employed i\ 
construction ; but we are not a' 
that it has ever been used in pracli 
Another claas of instruments, 
which tbe movable part ' 




Fia S.~ 

._ hotizontal arm taming abont a vertkal 

, may be looked upon as the descendants of Gilbert's electio- 
scoptc needle. The electrometer of Peltier and its modiGcation 
into a sine electrometer (by Riess} are instmments of this claai. 
Descriptions of botb will be found in Mascart, {J £fil and S92. 

Dellmann's electrometer (fig. 7} is constructed on a prinetple IMI - 
similar to that applied in the two instruments last named. D is a mlib 
needle, formed of light silver wire, suspended by a fine glass fibre 
from a torsion head A. Below tbe needle is ajiiece of sheet metal 
XE, divided half throDgh by a notch in tbe middle, and then bent 
in opposite directions On both aides of tbe notch, so that, when 
looked at end on, it appears like a T. Undetneath NK ia a 



< IC was by no means safe to take tbii for oertain In tbs eld li 

OMnts, owing to the electrification of the glasa 
r PhU. Trartt.. 1772. 



ELECTROMETER 



119 



fiadiwtod diM PL, throagh the centra of nhicb umcb a eUss 
tabs F •appoTtmg HE!, so th*t it cm b« railed or a«pTen«l by a 
lever O. Iniidfl F ii s spring b]r means of which the lever H, 
which atna as electrode, can be connected oi disconnectod at will 
with the metal piece NE. The whole cootained in a metal case B, 
tlie lid of which is of glass, so that the position oF the needle D on 
the ETBduation PL caa be read off b; means or the lens M. To 
oae the lutrament, the case is connected with the earth, the needle 
it brought neaily at nglit anglee to NE, and ME ii raised by 




Fici. 7.— Dellmin's Electrometer. 
nieana of G till the needle is in contact with it ; then the electrode 
K is brought into comlnDDication with NE, and the bodr whose 
charge or potential is to 1)b meaaured ti connected with fc. T)ic 
connection with K Is then suppressed, and NE lowered; and the 
needle, now tree, is repelled by NE. If, by means of tlie lorsion 
head, we bring the needle along to a fixed position relative to NE, 
the electrical couple will be proportional tothesqajre of the chsrgc 
communicated to NE and D, i.t., to the square of the polentinl of 
the body connected with K, provided the cai«icity of the electro- 
meter be negligible compared with that ot tlie Lody, Hence the 
potential is taeasured by the sqnare root of the torsion on the 6bre 
when the needle is in a given position. 

The form of Dellmann's electrometer we have jnat described was 
that used by Eohlrausch.' It hu been simpliSed by its inventor, 
and applied in his important inveitigatiooa on atmospheric elec- 
tricity. 

UoalomV* tnlance might be tised osanelectrometeron the rcpul- 
uon principle. Special care would, howerer, be necessary to avoid 
or to allow for disturbances arising frotn the case of the instrument, 
which Duaht under any circumstances to be coated wholly or pai- 
nallj with tinfoil on the Inside, according to Faraday's plan. Sir 
Wm. Thomson did, in fact, design an electrometer of thisdescrip- 



11. AttraeUd tHte £Utlr<mtltrt.—The first idea of litis kind of 




Fta 8.— Snow Banls'a Disc Elsctromelar 
Initniment is doe to Sir Wm. Snow Harria. One of theinstrti- 
meiita in which he carried out the prrociple and the mode of using 

) Pva. Anm., 1S13 and 18S2. 



it will be understood from Jig. S> C is an insulstcd disc, over 
which is suspended another disc, hung from the arm of a balance, 
and connected with the earth. A weight id ia put in a acalo 
attached to the other arm of the balance. The insnlsted disc ■■ 
connected with the intemat armaturo Ii oF a Leyden jar, whoMt 
outer armnliire is in connection with the suspended disc. Else- 
tricitv is conveyed to B, and the quantity q measared by s small 
Lane s jar A, nnlU the electric attnction at C is Just sufficient to 
turn the balance. Snow Harris found that ict ?'. This and other 
laws established by him ogiee with the molhematicnl theory u 
developed in the article ELBCTHCcirv.' 

Crest improvements have been effected in this kind ot electro- 
meter by Sir Wm Thomson— (!) by his invention of the "guard 
nng " or " guard' plate ; " (2) by using the torsion of a plstinutn 
wire for the standard force ; (3) by devising proper means for 
attaining a definite standard potentiul, and by protecting the vital 
parts of the electrometer from extmneoua disturbance ; and (0 by 
mtioducing sound kinematical principles into the construction ot 

In ordei to ;illuatr5lo these points it will bo well to describe the Thom- 
port.nble electrometer (fig 9), one of his simpler instruments, in son's 
iletnil portable 

The principal electrical parts of this electrometer are sketched in electro- 
fig 10. HH isa plane Jisc of metal (called the "guard pUie'Vnwter. 
kept at a constant |h> 
tential by being fixed 
to the inner coaling of 
a small Leyden jar IIM 
(fig. 9), whicli fontiii 
the case of the instiu- 
nicnt. At F a nqitnu' 
. of Mil. 






. fits, as 



nearly as it can without 
danger of touching, a 
square piece of alumi- 
nium foil as light as is 
conaiateut with pro|>er 
slifTness, One aide ol 
this disc is bent down, 
and then runs out hoii- 
mnUlty into a narrow 









) lieatridden 
if the ! 



The 



Ou 




Ihe enamel are two small dots very near each other. When &a 
hair seen throileh a small convex lens appears straight, and bi- 
recta the distniice between the dots, the Flimtp is said to be In 
the sighted |>usition. The alumi- 
nium spade is suspended on a hori- 
zontal platinum wire slretcheit by 
platinum springs nt its two ends, 
and is carefully balanced with its 
centre of gravity in Ihe line ot 
suspension, so that the only Force 
other than electric that ran affect it 
ia the torsion ot the wiie, which 
ecla like the strint; in the toy called 
the "jumping frog," ci like Ihe liaii 
rope in the uulapultaof thrsntienl". 
The spade is so arranged lliat P is 
as neatly as possible 



by the 



■ this 



posit 




remaining important electrical pan is the plane horizontal disc 0. 

It ia essential to the aclioa of the instrument (hat we should ba 
able to move the disc G parallel to itself aad to 1111 througli 
measared distances. Tlie mechanism h^ which this is accomplished 
is a remarkable initnncc of the ap]dication of geometriculprinciple* 
to mechanism, and the reader will do well to read Thomson's 
" Lesson to the instrument makers" on this subject in the Reprint 
of his papers, 3 309. The glass stem which carries G is filed into 
the loner end ot a hollow brass cylinder ; in the upper end of the 
cylinder is fixed a nut AC, through which works a carefully cat 
screw ending in a rounded point B of polished steel. The point B 
rests on a horizontal agate plate let into a foot which projects From 



• See :iIio Itrprtnt ot Sir Wm. 1 



■s Papers, f 168. 



120 



ELECTEOMETBE 



astroog vertical support fBatened to the bta«iid ot thsjarMM 
(fig. 9), and passes through a slit in tbe hoUow cylinder. This 
Tertioal piece is fitted on one side with tno V Dotchea, into which 
the hollow cylinder is pressed by a. sprine f&atsDed to the lid and 
bearing half way between the Vs. and on the other side with a rect- 
aogular groove in which slides the vertical part of a Icnee-piece D, 
Id rigid connection with the hollow cylinder. D prevents the 
cjlioder from turniDf; round, but allows it to move vertically ; it 
also carries a fiducial mark running opposite a graduation on one 
edge oF the groove, by means of which whole tuma of the screw are 
read off, fractions being estimated by means of a drum head. The 
~""' '" ' Lged in two parts, with a spring between them, to 



steadiness (for details, see paper 




prevent "lost 
cited above.) 

The disc is 
the main electrode S, which 
a glass «tem. The arrange- 
ment of this electrode is 
worthy of notice, and will be 
nnderetood from fig. 11. The 
dome T is called the nm- 
brella ; its use is obvious. A 
■imilar, only less perfect, 
devico was noticed in Ca- 
tbIIo's electroscope. The vital 
p*rta of the instrument are 
all inside tbe coated jar, and 
therefore removed from dis- 
turbing inflnencea ; only it 
ia necessary to remove some of 
tbe tinfoil opposite the bait 
in order to see iL The effect 
of this is counteracted by 
meatu of a screen of fine 

« anil the theory of 

simple. The body whose 
potential is to be measured 
u connected with the um- „„ ,, 

breUa, which is raised in '^- "' 

Older to insulate the main electrode from the case, the last being 
•npposed to be in connection with the earth. Let « Iw the poten- 
tial of the inner coating of the jar, the disc, and guard plate, V 
tbat of the body and G, and d the distance between 5 and H when 
the hair is tn the sighted position. Then, since F may be regarded 
as forming part of «n infinite plate,' if its surface be S its potential 
energy wUl be i3»(B VJ (see Electhiciiy, p. 8*), i.e., 
8(1'- V) ' 
Sird - 
Hence the attraction /on F will be given by 

^-^i^ <.>•■ 

Here/is a constant, depending on tbe torsion of the suspending 
wire of the aluminium balance ; bence, A' standing (or S>/-;-3, i.e., 
A being a conaWnt depending on tbe conatmctioo of tbe instrument, 
we have 

B-V^AJ (2). 

If we now depress the umbrella, so as to bring Q to the potential 
of the earth, and work the screw till the hair is again in the sighted 
portion, we have, tf being the new reading of the screw, 

v~Ad- (S), 

Bence, from (Z) and (3), 

V-A{d--d) W. 

We thus get V in terms of A and the difercTice of two screw read ■ 

ings, so that uncertainties of zero reading are eliminated. The 

value of A must be got by comparison with a standard instrumant, 

il absolute determi Dal ions be required. 

AbMlote Thomson's absolule electrometer (lig. 12) is an adaptatioo of the 

glw;tn,- attracted disc principle for absolutedelerminatious We give merely 

meter. ^ indication of itsdiireren t parts, referring to Thomson s paper (I.e.) 

for details. B is an attracting disc, which can be moved parallel to 

itself by a screw of known step (^ in. ot thereby). A is a guard 

plate, in the centre of which is a circular balance-disc of aluminium 

auspended on three springs, and coanecled by a spiral of light 

Slatinum wire with A. The disc can be raised or depressed into 
efinite positions by means of a screw (the kinematical arrange- 
ments in connection with these screws are similar to that in Die 
Egrtable electrometer). A hair on the disc, an object lens A, a 
ducial mark, and an eye lens I enabl e the observer to tell when 
' Those who deilce to know tbe degrta of approdmatlon here 
should oontolt Maiwell, Skctridly and Magiulitm, voL i. g 317. 



__ .ware the 

disc from electric diaturWcea. An idiostatic gnsge (co 
an aluminium lever with guard plate, hair, and lens, ma In tha 
portable electrometer), placed over a plate F in connectioD with the 
guard plate, enables the observer to tell when the guard plate and 
the inside coating of the instrument (which fortos a Leyden jar as 
in tbe portable instrument) are at a certain definite potential. 
And finally, a small instrumeot .called tbe " repleniaher ' enable* 




Fio. 12.— Thomson's Absolute E1ectromet«r. 

him to raise or lower the potential of A till this definite potential !■ 
reached. 

A short description ot the Tcplenisher will be in place bcR. It Repir 
ia represented pretty clearly at E (fig. 12). Two metal shields, |sh«r. 
in the form of cylindrical segments, are insulated from each other 
by a piece of ebonite ; the left hand one is in connection with the 
guard plate, the right hand one with the case of the instmmeot 
(and therefore with the outer coating of the jar), A vertical shaft, 
which can be spun round by means of a milled head, carries two 
metal flies on the ends of a horizontal arm of vulcanite. Two small 
platinum springs (the front one is seen at e) are arranged so as to 
touch Iho dies simultaneously in a certain position just clear of the 
shields. Let us suppose tbe left shield along with A to he posi- 
tively electrified, and the flies to be in contact with the springs : < 
being close to tbe left shield, tbe front flf will be electrified - and 
(be back By -t-. Suppose the abaft to revolve against the hands ol 
a watch lying face up on tbe cover of the electrometer. The front 
(ly carries off its- charge, and, when near 

shield, cotr " ' "' '"" "" 

Being thus 

-f charge to the left shield. The result of one levolution therefon 
is to increase the + and - charges on the respective sbielda, or, in 
other words, to increase tbe difference of potential between tbiem. 
By giving the machine a sufficient number of turns, tbe potential 
of A may be raised as mnch as we please ; and, b; spinning in tbe 
opposite direction, tbe potential can be lowered ; so that, onos A if 
charged, it is easy to adjust its potential till the hair of the gang* 
is in the sighted position. 

To work the instnimont, the electrode n of the lower plala B il 



BLECTROMETEE 



121 



'o the Mghtcd position. 





Fia 13.— Drr Pile ElMtroKopa. 

■nil the nppcr screw reading taken ; then a w«1ght of ^e gttmmM 
is dirtribnted lymmelrically on the disc, the mIum broaght Dp 
■gun b; woikiDg the acreir, snd the nading igND taken. We 



thn« aacertsin how far the weight of u mmmet depreuM Um 
lahuice. Tlie weight ii new remoTed, and the balance leftat a 

diBtanceiboTe A equalto that jiutfonnd. 

A is DOW charged, and iti potential 
adjusted till tbe haii of the gaoge in- 

I dicates that the atandard poteutial v is 
reached. Let it now be rtqaired to 
meaanra the diSerence between Uiepotm- 
tiala V and T' of two condncton. Con- 
nect Ent one and then tbe other with ft, 

I and work the lower screw till tbe hair 
of the balance iiiisbtedin each case, and -~-- ■■— 

let the ecrcw readings rednced to cenU- » < j 

metrea be d and i. Then, since tbe 

farce on the diK in each case is aw, where g is the acoaletatlon 
prodnced h; gravit; in a falling bodj in centimetres per second, we 

h»T8hy(l) 

V-V'-{d'-rf)y?^ .... (6), 

where S denotes the area of the balance disc, or rather the mean of 
the areas of the disc and the hole in which it works. We thus get 
the valne of V-V in absolute electriMtaticC. G. 8. anits. 

III. ST/mmelriail Elatronuttn. — Two ilLatmments fall to be Drj ftia 
described nnder Ihia head,— the dry pile electroscope, and Thomson's electto- 
qnadrant electromeUr. The idea common to these instruments Nops. 
is to measure differences of potential by means of the motions _ol 
an electrified body in a symmetrical field of force. In tbe dry pile 
electroscope, a single gold leaf is hung np in the field of force, 
between tbe opposite poles of two dry piles, or, in later forms <» 
the iDstrnment, of the same dn pile. The original inventor <rf 
this apparattls was Behreni, but tt often bears tbe name of Bohnen- 
berger, who slightly modifieii its form. Fechner introduced the 
important improvement irf aains only one pile, which be remoTed 
from Ibe immeiliate neighboiirnood of the suspended ImI. The 
poles of tbe pile ere connected with two discs ot metal, between 
which tlie leaf hangs. This anvngement makes it ea^er to aecure 
perfect symmetry m tbe electric fold, and allows oi to Tary tbe 
sensitiveness of the instniment by pUdng the metal pistes at 
diflerent diatancea from the leat In oidei l« make tbe attalnnuBt 




Pio. 1 E.— Ekratlon and Section of Thomson's Qnaditnt Bectlometer. 
of perfect aymmetry stiU more easy and ^rt"'" Rie«' «<lded a Hankel' still further improred the dry pUe electtoKope by slvini 



lurtal rod to the appantus, which 



mprovements, is repmented in 



icrometiic movement to the plates, ttr ■nbatttnting a gdvanie 
battery with a large number of ctll* for the uncertain and varying 
dry pile, and by naing a mlcroacope with a divided scale to measure 
the motions of the gold leaf. WjUi these improrements it became an 
SUelrvmdtr of gnat deUew^ and oonitdenble range. Some <rf tl« 



■ Haacan, 1 379, or J'ofg. Am 



122 



E Jj E — E L E 



« allndel to in th« ftrticlo 

Qnajnnt Id tli> qiuulraiit electrometer of Sir Wm. Thomson, vrbicli ii the 
electro- most delicate electro metric instrument hitherto invented, the 
moving bodjiia horizontal Sat needle aCalnmiainmfoi), Bnrronnded 
by n tiled flat cylindrical boi (fitr. It), which iadivided into four in- 
■nlated quadrenta A, B, C, D. The opposite pairs A, D and B, C are 
connected bj thin pUtinnm wires. The two liodies whose potentials 
ore to be compared are connected with the two pairs of quadrants. 
It A and B be their potentials, and C the potential of lie needle, 
it mav be shown (see Maxwell, Eleetriciiy and ifagn^tiiTn, f 218) 
that Uie couple tending to tnm the needle from A to B is 

a(A-B){C-i(AM-B)} (C). 

where a is a constant depending on the dimensions of the instru- 
ment. If C be very great compared with J(A + B), as it usually is, 
then the couple is 

«C(A-B) (7) 

mmply ; in other words, the couple varies as the diSbrence between 
the potentials of the qnadranta. Some idea of the general distribu- 
tion of the parta of tiie actual instrument may be gathered from 
fig. 15, which gives an elevation and a section of the instrument. 
The case forms a Ijcyden jar as osaol in Thomson's electrometers ; 
the intomal coating in this instance is formed by a quantity of 
concentrated sulphuric acid, which also keeps the inside of the 
instiument ilj. The qnadranta are sospended by glass pillam 
from the lid of the jar, and one of these pillars is supported on 
a sliiling piece, ammged on strict Unematical principles, so as to 
be movable in a horizontal direction by means of a micrometer 
BUew V. This motion is nsed to ai^ost the position of the needle, 
when chatted, so that its axis may fall exactly betweeo the qvtad- 
rants A, C, and B, D. A glass stem C, rising from the lid of the 
jar into a superatructnTe called the "lantern," supports a metal 
piece Z, to which is fasMned a metal framewoik fitted with supports 
and adjustments for the biGlar suspensLon of the needle. A fine 
platinum wire drops from the needle into the anlphiiric acid, thus 
couhectiog the needle with the inside coating of the jar. This 
tail wire is also famished with a vane, which works in the acid and 
damps the oscillations of the needle. A stout alumininm wire rises 
from the needle, carries a light concave minor T, and ends in a cross 
piece to which are atticbea the suspension fibres. The aluminium 
•tem and the platinum tail wire are defended from electrical disturb- 
ances by a gaard tube^ which is in metallic connection with the 
piece Z, BDif also, by means of a platinum wire, with the acid ; it 
u through this, by means of the "temporaiv electrode" P, that the 
inside of the jar is charmd. The two principal electrodes are P 
and M. Connected with Z Is a metal disc B, attracting the alu- 
minium balance of a gauge like thaftof the abaolnta electrDmet«r. 
This gaoge is well seen in the bitd'*eye view given in Gg. IS. A 




I's Qoadrant Electrometer— Bird's-eye view. 



r^Ieniaher, like that in the abaolate electrometer, is fitted to the lid 
of the jar, and by meana of it the potential of the needle can be 
4iastea till the hair of the guage is m the sighted position. 






_ le deflections of the inatmment are read off by ^. 

fonned by the mirror T on a scale at the distance of ■ metre or so, 
the abject being a wire which is stretched below the ecale in a slit 
illuminated b; a lamp. Within certain limits the deflections are 
proportional to the deflecting couple, i.e., to the difference between 
the potentiala of the qnadranta A, D and B, ; bnt where this is 
Dot BO, the instrument can easily be graduated experimentally. 

For many purpoees, eapecially in theleotnra room, an initrament 



complicated as the abora is nnnecMUUT and imdMlnhla, A 
■-iler form (fig, 17) of qmuJrantelc"' — — -'— ' '- - — • 

miot Brothera, uid answers KM 

ipitlary SUdromila-a. — Elec- 

leters have recently been con- 
structed by taking advantage of 
the fact that the aarface tenmon 
of mercury is greatly aflected b^ 
the hydrogen deposited on it 
when It is the negative electrode 
in contact with lulute sulphuric 
add (see £lbctboltsis, p. lOS). 
A qnantity of mercury is placed 
in the bottom of a test tube, and 
commnnicates with a platinum 
electrode let in through the bottom 
of the tube ; on the mereurj is 
poured dilute sulphuric acid, and 
into this dips a tube drawn out 
into a capillaiy ending. This 
tube contains mercury down to s 
certain mark on the capillary pwt, ... 

the remainder being occupied '■ 

with acid which is continuous with that in the test tube. 8o long 
as the mercury in the test tube is simply in metallic connection 
with that in the upper tube, the posiboa of the mercuir in the 
capillary part ia stationarjr ; bnt if an electromorive force be intro- 
duced into the external circuit, acting towards the test tnbe, then 
hydrogen is deposited on the small mercmy surface, its sor&ce 
teosion increases, and the pressure in the tube most be considerably 
increased to maintain the mercury at the mark. This increase of 
pressure is proportional to the electromotive force within certain 
limits, hence we can use this arrangement as an electrometer. 

ElatTometrie MeaauremerU. — Several examples of electrometrie 
measurement will be found in the article Electricity (pp. 18, S7, 
3S, 42, ^iK.]. We recommend in this connection the stady of 
tlie sectto3Kon atmospheric electricity in Sir Wm. Thomson's Bt- 
priid of Papen on BUclridty and Magnairm, and section* SSO 
and 22S in Cberk Maxwell's Elittnaty and MagnOitm. We have 
been drawing throughout qb^ Thomson'* BepDri on Eitetnm^ert 
and BleclTomAic Meatarementt/Yni it will not be amiss to draw 
attention to itpnce more. , (Q. CH.) 




219 



MAGNETISM 



f rriHE word magnetism is derired from the Greek word 

' X ft ayi^, which was applied to an ore of iron possessing 

^ a remarkable attractive power for iroD, and supposed to 

have been origiaalljr found near the town of Magaesia, in 

Lydia.* Thus Lucretius writes: — 

Qnem Hagaeta vocant ^trio de nomine Graii, 
Hsgoetum qnia Gt patriu in Quibue ortua. 
This name is said by Plato ^ to have been given to it by 
Euripides, and he adds that moat call it the Heraclean 
stone. It is needless here to criticize the above or other 
derivations that have been given for the word ; we merely 
remark that it is now applied to all the phenomena kindred 
to that which first drew attention to the magnetic iron ore, 
vis., a aelectire attraction for iron. 
iT In the following article we shall give, in the first place, 
a sketch of the leading phenomena of strongly magnetic 
' bodies. We shall then deecribe a provisional theory suf- 
ficient to render a general account of these phenomena, 
and shall afterwards proceed to render this theory more pre- 
cise, to develop it to its necessary conclusions, end to com- 
pare these with experiment, indicating where the theory is 
either incorrect or incomplete. Then we shall discnss the 
paramagnetic ami diamognetic properties of all bodies, as 
expounded by Faraday ; an account will be given of the con- 
nexion between the magnetic and the other physical proper- 
ties of bodies ; and, lai^tly, we shall endeavour to give some 
idea of the difierent physical theories that have been pro- 
posed in order to give something more than a mere short- 
hand record of the facts of observation. 

Leading Phbnohena. 

tic It appears, from what Lucretius says in the passage 

above quoted,^ that the Greeks and Romans were aware, 

°' not only that the loadstone, or magnetic iron ore, attracted 

'' iron, but also that it endued iron in contact with it with 

its own peculiar property. Thus an iron ring will hang 

suspended by the attraction of a loadstone, and from that 

ring another, and so on, up to a certain number, depending 

on the power of the stone and the weight, &c., of the rings. 

They were also aware that the attraction was confined to 

iron, or at all events was not indiscriminate, and that it was 

not destroyed by the intervention of other bodies, such as 

brass, between the magnet and the iron. It appears, too, 

from the passa^ — 

Fit cgnoqne at a lipids hoc ferri Dstnra i«c«d»t 
Intcrdutn, fugere Btqns sequi consneta TiciaiiiD, ke. — 
that they had an idea that, under cert^n circumstances, 
the attraction might be replaced by a repulsion. If, how- 
ever, we understand aright the latter part of Lucretius's 
somewhat obscure description of what seems to have been 
an actual experiment of his own, this notion was in reality 
a hasty generalization, not justified by the observed facte.* 
In any case there seems no warrant for assuming, as some 
have done, that the ancients had any definite conception of 
magnetic polarity. 

What they wanted in definite experimental knowledge 
they supplied by an abundant use of the imagination. 



> 'Ev r)! A(«y Mr EbpurOm utr HoTrqTiv ^ri/iairir, ot Si 
'HfiiKktiar (/iM, G33D). Sm Uunio'i luereliiu. toL L ] 
lb* othar name ia from Haraelaa In Ljrdia. 

* Bk. vL lin« 90S *;,, and 1012 tq.; coinp. Plato, /m, hI 
vbom tbtra It tWMU to think ha ia qaottBO. 

* Baa Ulow, p. iSS. 



We are told, for instance, that the magnet attracts wood 
and flesh, which was certainly beyond their powers of 
observation; that it ia efTectiTS in the cure of disease; 
that it afiecta the brain, causing melancholy ; that it acts 
as a love philtre; that it may be used in testing the 
chastity of a woman ; that it loses its power when rubbed 
with garUc, but recovers it when treated with goat's blood ; 
that it will not attract iron in the presence of a diamond, 
and much else that was eagerly copied by the wonder-loving 
writers of the Middle Ages. 

The science of magnetism made no real progress till the 
invention of the mariner's compass. The early history of 
this instrument is very obscure. According to some autho- 
rities it was invented in China, and found its way into 
Europe probably through Arabian sources. The light 
thrown by recent researches on the literature of the Chinese 
has apparently thrown doubt upon their claim to this 
invention,^ although the knowledge of the loadstone and 
its attractive property may have been older among them 
than even among the Greeks. The first accounts of the 
compass in Euro[)e go back to the 12th century, and, 
although the instrument described is very rough, it is 
not spoken of as a new invention. In its earliest form 
it seems to have consisted simply of an iron needle which 
was touched with the loadstone and placed upon a pivot, 
or floated on water, so that it could turn more or lesa 
freely. It was found that such a needle came to rest in a 
poeition pointing approximately north and south (some 
accounts say east and west, in which case there must have 
been a cross piece on the needle to indicate what was pro- 
bably the important direction for the mariner). As these 
compasses were made of iron (st«el was not used till much 
later), end were probably ill-pivoted, they must have been 
very inaccurate; and the difficulty of using them must 
have been much increased by the want of a card, which 
was a later addition made apparently by the Dutch. 

It is unnecessary to enter into more detail here respectt- 
ing the early history of the compass, as the matter l)u 
been very fully treated in the article Compass. " Wo pm 
ceed therefore to show the bearing of the invention Hpon 
the science of magnetism. It will at once be seen that it 
involves two scientific discoveries of capital importance : — 
first, that the loadstone can transmit to iron with which it 
comes in contact a permanent property like its own ; and, 
secondly, that a loadstone or magnet if suspended freely 
will turn so that a certain direction in it assumes a fixed 
poeition relative to the geographical meridian, a certUD 
part of the magnet turning always towards the north, and 
the part opposite towards the sontL These oppoeite parts 
of the magnet are called its " polee." 

To fix our ideas we shall describe a proceea by which 
we might definitely determine this direction in the magnet. 
Following the example of Gilbert, lot ns consider a 
spherical magnet Our reason for dealing with this form 
in the first instance is to make it perfectly clear that the 
phenomena depend essentially on something apart from 
the form of the body. We shall suppose that the magnet 
is homogeneous as to its mass, bo that its centre of gravity 



Harion'a 

compaat. 



• Saa Uollaudorir, Z. D. U. O , iiiv. 70. 

* It nur 1" raantloaad that tha atal«muit that Pewr Adiiger, in 
a lettat wiitten in 1296, mantiooa tha magnatic dacUnatioD, appeara 
to be a miitaka, arising from the mtstnniieription of a titje. See 
Wenckebach, qaotad by I^mont, UanJbuck da J/Offnttitmitt, p. i49. 
The paiaage from Are Frode, qooted b; Uanatcan, and aliodad to in 
last adiUan of thia ancfclopndia, ^>paara alao to be of doubtful 
anti<pilt7. 8m PoggendoriT, OaacUdU* 4er Pkytik, p. 08. 



220 



MAGNETISM 



coincides with its centre of figure. Suspend this spherical 
magnet by a fine thread of untwisted silk, attached to any 
point of its surface, say P. After the magnet has come to 
rest, mark the vertical plane through the centre which falls 
in the geographical meridian ; this may be done by trac- 
ing a great circle on the surface of the magnet. Next 
find the point P' in which the vertical through P cuts 
the surface again, and suspend the magnet by F, again 
marking the plane which falls in the meridian. Now, 
find the plane which bisects the acute angle between the 
two former planes, mark it by a great circle, and call it 
the axial plane of P. If we thus find the axial planes of 
any number of points, we shall find that they all intersect 
in one common line passing through the centre of the 
sphere. We may call this line the " axis " of the magnet. 
Let us mark the points where it cuts the surface ; we may 
Poles, call these the ''poles" of the magnet We shall then observe 
north ^^^^^ however we suspend it, the magnet will always come 
^^lY^ to rest so that the vertical plane through the axis makes a 
definite angle with the meridian. This angle (3) is called the 
" declination " (also, by sailors, the " variation "); it varies 
from place to place, and from time to time, but very slowly, 
80 that throughout a limited area of the earth's surface, 
and for a limited time, it may be regarded as constant.^ 

One end of the axis always turns northwards, and the 
other always southwards; we shall call the former the 
"north" and the latter the "south pole," although, for 
reasons to be afterwards explained, it would be more appro- 
priate to invert the order of these namea Henceforth the 
vertical plane in which the axis of the magnet comes to 
Magnetic rest will be called the magnetic meridian, and the two 
meridian, horizontal directions in this plane magnetic north and 
magnetic south respectively. 

It must be carefully noticed that there is a certain 
amount of arbitrariness in our definition of the axis and 
poles of a magnet. In reality it is only the direction of 
the axis that is fixed in the body, and not its absolute 
position. This will be made plain if we repeat all our 
experiments with the spherical magnet after fastening to 
it a piece of wax or other non-magnetic body, so as to 
leave its magnetic properties unchanged, but to throw its 
centre of gravity out of the centre of figure. Everything 
will fall out as before, only the axial planes of the different 
points of suspension will now meet in a line, parallel, it is 
true, to the axis determined before, but passing through the 
new centre of gravity. In point of fact, therefore, we 
might choose any point in the body, draw a line through it 
in the proper direction, and call this the axis. Hereafter 
we shall, unless the contrary is stated, draw the axis 
through the centre of gravity of the body, or through its 
centre of figure if it has one ; and we define the poles, for 
the present, as the points in which the axis cuts the sur- 
face of the magnet, supposing, as will be generally the 
case, that the line cuts the surface in two points and no 
more. 
Magnetic Having now obtained a definite idea of the axis of a 
naedlo. magnet, and seen that it has, in the first instance at least, 
nothing to do with the external form of the body, let us 
proceed to make an artificial magnet of the particular kind 
usually called a " magnetic needle," and briefly examine its 
properties. Take a tolerably thin flat piece of pretty 
hard-tempered steel, of the elongated symmetrical form 
KS shown in fig. 1. We suppose it, in the first place, 
in an unmagnetic condition. Let it be pierced by a well- 
turned axis aby passing accurately through its centre of 
gravity, and perpendicular to its plane, so that, when the 

^ For the early observations on the declination the reader is re- 
ferred to the treatment of the subject of terrestrial magnetism in the 
article Meteoboloot. At the present time the declination at Qreen- 
TTich ijB a UtUe over IS"" ; at Edinburgh it woold be abont 4* more. 



axis is placed on two horizontal knife edges, the needle will 
rest in any position indiflferently. Further, let four very 
small hooks, c, d, e,/, be attached, two (c, d) to the ends 
of the axis, and other two (e,/) to the edges of the needle in 
a line perpendicular to NS. Now rub the half of the needb 




N<i nil"IM'I S!C 



■^ « 



aS 



T"^ 

d 
Fig. 1. 

towards N with the south pole of the spherical magnet 
whose properties we have just discussed, beginning the 
stroke at the middle and ending it at the point of the 
needle, and for symmetry's sake let us do the same to the 
other side of the needle, and then repeat this process 
with the north pole of the sphere on the other half 
towards S. Let us examine the properties of the needle 
thus " magnetized." If we suspend it first by the hook e 
and then by the hook d, we shall find that in both 
cases the line joining NS^ makes very nearly the same 
angle with the geographical meridian. Hence the mag- 
netic axis must lie in a plane through NS perpendi- 
cular to the plane of the needle. A similar experiment 
with the two hooks e, f will show that the magnetic axis 
lies approximately in the plane of the strip, which we may 
suppose for the present to be infinitely thin. Hence the 
magnetic axis may be taken to be coincident with the line 
NS joining the points of the needle. This coincidence 
is, however, in general only approximate, and in delicate 
measurements corrections have to be made on that account, 
of which more hereafter. If we now mount our magnetized 
needle on a piece of cork or two straws, and float it in a 
basin of water, or replace its axle by a small cap and set 
it on a pivot, we have the mariner's compass in its early 
form. We shall call it a magnetic needle, to distinguish 
it from the more elaborate compass of the present day. A 
favourite way of showing the directive property of a 
magnet, described by Gilbert, is to magnetize a sewing- 
needle, and lay it very gently, by means of a fork of wire, 
on the surface of ^ater ; it will float and turn until it takes 
up its position in the magnetic meridian. 

A needle mounted in this way, so as to have great freedom to 
move in a hori2ontal plane, is of crreat use in magnetic experiments. 
Gilbert calls it a * * versorium. ** When very delicate applications are 
in view, the point of the pivot on which it is mounted must be very 
hard (sav of hard tempered steel or iridium), and the cap should 
be fitted with an agate or other hard stone having a polished 
cavity of the form of a blunted cone to receive the pivot A still 
better arran^ment, also used by Gilbert, is to suspend a short and 
very light piece of steel wire — a fine sewing needle may be used — 
by means of a single fibre of silk. The most delicate arrangement 
of all is to use one of Sir W. Thomson's light galvanometer mirrors 
with the magnets attached, and follow its movements by means of 
the lamp ana scale as usuaL See Galvanometer. 

Such, with as much of modem accuracy imported into 
them as was necessary for clearness of exposition, were the 
facts of magnetism as known up to the beginning of the 
16th century. 

Another experiment with our magnetized needle willl^^ 
enable us to describe the next important magnetic clis ^^ 
covery. In its unmagnetized condition the needle rested 
indifferently in any position when its axis was placed oq 

' Or the vertical plane through it, should it happen to be not quit* 
hoiizontaL 



MAGNETISM 



221 




Tig. 2. 



two horizontal knife edges. In the magnetized state this 
is no longer the case. The axis of the needle now takes 
up a fixed position, with its north 
end pointing downwards (fig. 2)| 
and if disturbed will oscillate 
about that position, and finally 
settle into it again. The angle 
which the axis NS makes with the 
horizon is least when the plane of 
rotation of the needle is in the mag- 
netic meridian : the angle (t) in this 
case is called the '' dip/' or (by Con- 
tinental writers) the ''inclination.'' 
It is greatest, viz., 90% when the 
plane of rotation of the needle is 
vertical and perpendicular to the 
magnetic meridian. At Greenwich 
the dip is about 67^ 30' at the pre- 
sent time. If we place the needle 
with its plane of rotation perpendi- 
cular to the line of dip, the equili- 
brium will be indifferent, as it was 
in all positions before magnetization ; but there is no 
other position of the magnetized needle for which this 
is true. 

The remarks which we made as to variation in space 
and time of the declination apply also to the dip. The 
variation from place to place differs, however, in nature 
from that of the declination. Along a line running in the 
neighbourhood of the geographical equator, partly north 
and partly south of it, the dip is zero. North of this line, 
which is called the magnetic equator, the north end of the 
needle dips below the horizon ; and the angle of dip 
increases as we go northwards, until, at a point in the 
Hudson's Bay Territory, the needle dips with its north 
pole vertically downwards. South of the magnetic equator 
the south end dips below the horizon ; and there is 
again a point in the southern hemisphere where the south 
end dips vertically downwards. These points are called 
the "magnetic poles " of the earth. For further details 
on this subject we refer the reader to the discussion of 
terrestrial magnetism in the article Meteorology. 

It was in the accurate observation of the declination and 
dip of the magnetic needle that the science of magnetism 
arose. The dip appears to have been first observed by 
Georg Hartmann, vicar of the church of St Sebaldus at 
Nuremberg (1489-1564), who seems to have been in 
advance of his age in magnetical matters. In a letter^ to 
Duke Albrecht of Prussia, dated 4th March 1544, he 
writes:— 

" Besides, I find this also in the magnet, that it not only turns 
from the north and deflects to the east about 9"" more or less, as I 
have reported, but it points downwards. This may be proved as 
follows.^ I make a needle, a finger long, which stanas horizontally 
on a pointed pivot, so that it nowhere inclines towards the earth, 
bat stands horizontal on both sides. But as soon as I stroke one 
of the ends (with the loadstone), it matters not which end it be, 
then the needle no longer stands horizontal, but points downwards 
i/dllt unter skh) some 0** more or less. The reason why this 
happens was I not able to indicate to his Royal Msgesty." 

From this it will be seen that Hartmann had unques- 
tionably observed the tendency of the magnetized needle 
to dip. His method of observing is of course unsuited for 

" Brought to light by Moser. See Dove's Repertorium der Phytik, 
ii, 1838. It does not appear that Hartmann's letter was ever 
before published. Moser is therefore scarcely justified in attackiug 
Norman's priority in this matter, still less in attempting to deny him 
the credit of first observing the dip by a sound method. Had he read 
the Newt AUraetive he could scarcely have fallen into such an error ; 
for in respect of clearness and scientific precision Hartmann's letter, 
interesting as it is, cannot for a moment be compared with Norman's 
UtUe work. 



fnecuurement^ and it is not surprising that he got a result 
of 9° instead of somewhere about 70\ 

In 1576 the dip was independently discovered by Robert Norman. 
Norman, a skilful seaman and an ingenious artificer, 
according to Gilbert He was in the habit of making 
compass needles, and carefully balancing them so as to 
play horizontally on their pivots before magnetization. 
He found that, after they were magnetized, they constantly 
dipped with the north end downwards, so that a counter^ 
poise had to be added to bring them back to the horizon. 
Thb led him to construct a special instrument, the proto- 
type of the modem dipping needle, to show this new 
phenomenon. With this instrument he made the first 
accurate measurement of the dip, and found it to be 71*" 
50' at London.^ 

The early English magnetic observers, of whom Norman 
and Burroughs (who wrote an able supplement to Norman's 
work) were admirable examples, must have done much for 
the introduction of precise ideas into magnetism. But their 
fame was speedily eclipsed by William QUbert of Colchester^ Gilbert 
(1540-1603), whom Poggendorff has justly called the 
Qalileo of magnetism, and whom Galileo himself thought 
enviably great In his great work entitled De Magiiete 
MagneticUgue Corporibus et de Magna Magnete Tellure 
Fhpsiologta Nova, first published in 1600, we find a com- 
plete account of what was known of magnetic phenomena 
up to his time, with a largo number of new ideas and new 
experimental facts added by himself. We find in Gilbert's 
work, in a more or less accurate form, nearly all that we 
shall lay before the reader in the first section of this article, 
described very much in the language that we shall use. 
" How far he was ahead of his time is best proved by the 
works of those who wrote on magnetism during the first 
few decades after his death. They contributed in reality 
nothing to the extension of this branch of physical science.'' ^ 

Mutual Action of Like and Unlike Poles, — If we take a Like 
magnet whose poles N', S' have been determined and ™*8P=»«tlo 
marked as above explained, and bring its north pole N'JJ^^. 
near the north pole N of a magnetic needle, N wiU move unlike 
in a direction indicating repiUsion between N and N'. attract 
The same result will follow if the south pole S' of the 
magnet be brought near the south pole 8 of the needle. 
But if S' be brought near N, or N' near S, attraction will 
be indicated. Hence the 
following fundamental law 
of the action between two 
magnets : — Like poUs repel 
each other; unlike poles 
attract each other. It would 
appear, therefore, that the 
whole action of one magnet N 
upon another is of a some- 
what complicated character, 

even if we take the simplest j^>l^ ^-^^ <;i 

view of it that the experi- 

mental facts will allow, viz., ^^' 

that the action may be represented by forces acting between 

the two pairs of points in each magnet which we have 

defined as north and south poles. On this assumption, 

the action of N'S' upon NS would consist of the four forces 

represented in fig. 3, for all these must exist in accordance 

with the law just established. Whether this is a sufficient 

* He published a work, of which the following description is given 
in the Ronalds* Catalogue : — " The Newe Attractivt, containing a short 
discoarse of the Magnes or Lodestone, and amongst other his vertues, 
of a new discovered secret and subtill propertie concemyng the 
Dedyning of the Needle, touched therewith, under the plaine of the 
Horizon. Now first found out by Robert Norman, Hydrographer. 4to 
(black letter, scarce), London, 1581." 

* For details as to his life, see art Gn^SRT. 
« Poggendorff, OuchichU der Physik, p. 286. 




MAGNETISM 



repreeentatiun ot Uie most general case, and what the exact 
law of the forces ought to be, we are not yet in a position 
to decide. One thing, however, is clear, that the action 
between two poles must diminish when the distance between 
them increases ; otherwise we should not have been able 
to make the action of N or S upon N' prevail, hy bnnging 
the one or the other nearer. 

It was perhaps the complexity of this analysis (along 
with the fact that the action of the magnet upon soft 
iron, which waa the earliest discovered magnetic pheno- 
menon, is not a pure case of this action, but involves 
also another phenomenon, viz., magnetic induction) that 
prevented for so long the discovery of the elementary \iw 
we are now discussing. At all events, it seems to ha^e 
been a new discovery in the 16th century, if we may judge 
from a passage in the letter of Hartmann above alluded to 
He was certainly aware of the existence of magnetic repul 
aion in some form or other. It is somewhat difGcult to 
gather from his description what it was exactly that he 
observed, and be nowhere atates the law fully and exphcitly 
In Norman's Newe Attractive ^ we find it dearly Etated, 
and demonstrated by means of a needle floating on water 
or suspended by a thread;^ yet be does not appear to claim 
the fact as his discovery, li, therefore, Hartmann was not 
the actual discoverer, we may at least conclude that the 
law became familiar to magnetic philosophers during the 
thirty years that separated him from Norman. 
HippiDg The Magnelie Field. — We nest introduce a method of 
ont the conceiving and describing magnetic actions which was 
^J^*"*^ invented and much used by Faraday. Since a magnet acts 
upon a magnetic needle placed anywhere in the surround- 
nMgnetic '"8 apace,' we call that space the magnetic field of the 
force, magnet Neglecting the earth's magnetism, we may map 
out this field as follows. Conceive any plane drawn 
through the axis of the magnet, and place it so that this 
plane shall he horizontal Then at any point in this 
plane place a veiy small magnetic needle, and note the 
direction which its axis assumes under the action of the 
magnet; then proceed to move the centre of the needle 
in the direction in which its north pole points, and con- 
tinue the motion so that at each point the centre is 
following the direction indicated by the north pole. The 
line thus traced will at last cut the surface of the 
magnet at some point lying towards its south pole ; and if 
we continue the line backwards, by following tiie direction 
continually indicated by the south pole of the needle, it 
will cut Uie surface of the magnet at some point lying 
towards the north pole. Such a line is called a line of 
magnetic force ; and, since one such line can be drawn 
through every point of the plane, and any number of 
planes can be taken through the axis of the magnet, we 
can conceive the whole magnetic field filled with such lines. 
Fig. 4, taken from Faraday, gives an idea of the distribu- 
tion of the lines of force in the field of a bar magnet ; fig. 
6 represents the lines in the field due to two neighbouring 
like polea 

These diagrams were not obtained by the method we 
have just described, but by s much simpler process which 
we shall describe by and by. Their use, so far as we have 
gone, is to tell us bow a small needle, free to move about 
its centre in any direction, will place itself at any part of 
the field, viz., it will place its axis along the tangent to 
the line of force which passes through its centre, its north 
pole pointing in that tUrection which ultimately leads to 
the south pole of the magnet producing the field 
Tenlla Suppose we apply these ideas to a spherical magnet (a 
or idwl terella, or earthkin, as Gilbert calls it). The lines of force 

earth. '- 

' Chip. L 

■ Sea alio Gilbert, D» MagiuU, Ub. L up. t. 

* OUbert otu th* phnu ortit nrhtti Id a tomewbat tlmllar Mue. 



in any plane through its axis wonld be found to mn some- 
thing like the curves in fig. 6 If, therefore, wa earned a 
small needle (suspended from a silk fibre so as to be 
perfectly free to move m all directions) round the magnet 




ID a moridiBQ plane, its axis would couElautly remain in the 

rneridian pkno, its north pole always point towards the 
Bonth pole of the Bphericfil magni^t, but dip more and more 




below the tangent plane to the sphere as the centre recedes 
from the equator, and end by pointing straight towards 
the south pole when the centre reaches the magnetic axis 




When we reflect that in all our eiperimenta HlB pro- 
perties of magnets, whether native, sudi as the loadatona^ 
or artificial, such as the needles magnetized by rubbing 
with the loadstone, have proved alike^ and ttiat vnrf 



MAGNETISM 



223 



purely magnetic action on a magnet has its aource in some 
other magnetic body, we are naturally led to the con- 
clusion that the reason why at every point of the earth's 
surface the axis of a freely suspended magnet assumes a 
definite position is simply that the earth itself is a great 
magnet, and that in observing the declination and dip we 
are simply exploring the magnetic field of the earth. It 
is true that, according to the experiment above described, 
the declination would every where be zero, and the magnetic 
equator would coincide with the geographical, but that 
arises merely because we assumed our earthkin, for 
simplicity of explanation, to be symmetrically magnetized, 
80 that its lines of force ran in planes passing through its 
axis. It remains to be discussed whether the most general 
assumption, viz., that the earth is a magnetic body, will 
not account for the facts of terrestrial magnetism. The 
answer to this question has been given, as we shall see, by 
Gauss. 

This idea, whose simplicity is the truest measure of its 
greatness, is due to Gilbert, and was by him made the 
foundation of his work on magnetism. The boldness of 
his theory will be appreciated when we remind the reader 
that in his day the dip was but newly discovered, and had 
been measured only at London, so that Gilbert's very full 
and clear exposition of this phenomenon, which we have 
given above, was in fact a scientific prediction, which was 
not fully verified till long afterwarda^ Before Gilbert a 
variety of wild conjectures had been made as to the cause 
of the directive property of the magnet^ Many, like 
Colambus, Cardan, and Paracelsus, believed that the 
magnet was attracted by a point in the heavens, possibly 
some magnetic star. Others supposed that the attracting 
point was situated in the earth; Fracastorius imagined 
hyperborean mountains of loadstone situated near but not 
quite at the north pole; and to this theory others con- 
tributed the detail that the magnetism of these mountains 
was so powerful that ships in these regions have to be built 
with wooden nails instead of iron ones, which would be 
instantly drawn out by the magnetic attraction. 

It is clear that, if we call that magnetic pole of the earth which 
lies in the northern hemisphere its north pole, we ought, in accord- 
ance with our fundamental law of magnetic action, to call the north- 
seeking pole of an ordinary magnet a BoiUh pole. When it is 
neoeasaiy to speak of magnets from this point of view, the diffi- 
culty is got over by calling the north-seeking pole the austral pole, 
and the south-seeking pole the boreal pole. In reality the danger of 
confusion is more imaginary than real. The reader should be warned, 
however, that in some French works the ordinary nomenclature is 
reversed, and that Faraday uses '' marked " and " unmarked," and 
Airy "red " and '* blue," in the sense in which north and south are 
commonly used. 

h*i Th^ Earth's Action on a Magnet is a Couple, — Norman 
* of in his Neive Attractive (chapters v. and vL) discusses very 
s^ acutely the question whether there is any force of transla- 
tion exerted upon a magnet. He advances three conclusive 
experiments to prove the negative. First, he weighed 
several small pieces of steel in a delicate gold balance, and 
then magnetized them, but could not detect the slightest 
alteration in their weight, " though every one of them had 
received vertue sufficient to lift up his fellow." Secondly, 
he pushed a steel wire through a spherical piece of cork, 
and carefully pared the latter so that the whole sank to a 
certain depth in a vessel of water and remained there, 
taking up any position about the centre indifferently. 
After the wire was magnetized very carefully, without 
disturbing its position in the cork, it sank to the same 

^ TYm first verification was by Hudson, who, in 1608, found the dip 
in 75* 22' N. lat. to be 80° 80'. Gilbert found 72** at London in 1600. 
The place of vertical dip in the northern hemisphere was first reached 
by Sir James Ross in 1831. It was found about 70*' 6' 17" N. lat 
and 96* 45' 48" W. long. 

s See GMlbert, De MoffneU, Ub. L cap. L 



depth as before, neither more nor less, the only difference 
being that now the wire set itself persistently in a definite 
fixed direction parallel to the magnetic meridian, the north 
end dipping about 71^ or 72"^ below the horizon. Thirdly, 
he arranged a magnetized needle on a cork so as to float 
on the surface of water, and found that, although it set in 
the magnetic meridian, there was not the slightest tendency 
to translation in any direction.^ He concludes that thero 
is no force of translation on the magnet, either vertical or 
horizontal He was evidently somewhat puzzled how to 
put this result into a positive form, and his ''point 
respective,'' as he calls it, is not a very clear explanation of 
the earth's action. What he wanted was the modem idea 
of a '^ couple," t.f., a pair of equal but oppositely directed 
parallel forces acting on the two ends of the needle ; but 
such an idea was not conceived in Norman's day. Gilbert 
adopts Norman's result in this matter, adding nothing 
essential, reproducing even Norman's diagram of the 
spherical cork with the wire through it It is clear 
therefore that Gilbert had a forerunner in the practice, as 
Bacon had in the theory, of inductive science ; for Norman 
says, speaking of the mass of fables that had passed for 
truth in geography, hydrography, and navigation before 
his time, " I wish experience to bee the leader of Writers in 
those Artes, and reason their rule in setting it downe, that 
the followers bee not led by them into errors, as often- 
times have beene seene." 

The Magnetic Property is MoleaUar. — Apart altogether Magnet- 
f rom the question as to how we are to represent the action ^*™ * 
of a magnet upon other magnets, there arises another quite ^^^^ 
distinct question, as to where the cause of this action 
resides. That these two questions are really distinct, 
although there has always been a tendency in the more 
superficial treatises on the subject to confuse them, will be 
obvious from the fact that we shall afterwards obtain more 
than one perfectly general way of representing the action 
of a magnet at external points, whereas there must be one 
and only one cause of this action. A very old experiment * 
at once throws considerable light on this point If we 
break a bar mag- ^ ^ 

net into two i » 

pieces, it will be ^ 
found that each [ 
of these is itself ^^ 
a magnet, its axis 
being in much 
the same direo- 






N' 



C 



S'N' 

Ike 



3CI 



T 



Fig. 7. 



tion as that of the original magnet, and its {>oles in cor- 
responding positions, see fig. 7. The same holds if we 
break the bar into any number of pieces; and, quite 
generally, if we remove any piece, however small, from a 
magnet, this piece will be found to be magnetic, the direc- 
tion of its axis usually bearing a distinct and easily 
recognizable relation to the direction of the axis of the 
whole magnet We are therefore driven to the conclusion 
that the magnetic quality of a body is related to its ultimate 
structure, and not simply to its mass as a whole, or to its 
surface alone ; and this conclusion is not to be invalidated 
by the fact that we can in general, as will afterwards 
appear, represent the action of the magnet at external 
points by means of a proper distribution of centres of 
attractive and repulsive forces upon its surface merely. 

Temporary Magnetism of Soft Iron and Steel in the 
Magnetic Field. — Bodies which possess permanent magnetic 

* Hartmann (see his letter above cited) was in error on this subject 
Ue describes a somewhat similar experiment, and distinctly states that 
the needle has a motion of translation. '*Schwimmt mit dem Ort 
welcher ist mittemlichtlich am Stein, bis er kam an den Port der 
SchMssel, da das Wasser in war." 

^ Cy. Gilbert, De Magnett^ lib. L cap. v. 



224 



MAGNETISM 



induc- 
tion. 



Magnetic properties, not depending on the circumstances in which 
they are placed, we shall henceforth call "permanent 
magnets." The law of the action of one permanent magnet 
upon another, as we have seen, is that like poles repel and 
unlike poles attract each other. The action of a permanent 
magnet on pieces of soft iron is, at first sight, different, for 
either pole attracts them alika 

To fix our ideas let us take a small thin bar of soft iron 
or of steel, and test it with a delicate magnetic needle. It 
will usually be found, more particularly if a steel bar is 

diu^lon. taken, that one end of the bar will repel one or other of 
the poles of the needle. Thb is a sure sign of permanent 
magnetism. If, -however, we heat the bar to whiteness 
and allow it to cool in a position perpendicular to the 
earth's magnetic force, 



Experi- 
ments 
illostrat' 



all permanent magnet- 
ism will be found to 
have disappeared. If ^ 
we now place the bar <= 
in a horizontal plane 
(fig. 8) with its axis 
perpendicular to the 
axis of the needle, and 
one of its ends A, B 
near either pole of the 
needle, that pole will be 
attracted, no matter 
whether it be the north 
pole or the south pole 
of the needle, or which 
end of the bar be used. 



JV 



fi 




Fig. 8. 



Care must be taken in this experiment to avoid using a too 
strongly magnetized needle, and to keep the needle from 
touching the bar, otherwise the bar may receive traces of 
permanent magnetism which will disturb the restdt It is 
very easy, by repeating the above experiment with an un- 
magnetized needle, to show that the power that the bar 
acquires of attracting the poles of the needle is temporary 
and depends on the presence of a magnetized body. 

Keeping to our principle that a magnetic cause is to be 
sought for every magnetic action, we are led to explain the 
above experiment by saying that in the magnetic field a 
bar of soft iron or of unmagnetized steel becomes magnetic 
in such a way that its north pole points as nearly as may 
be in the positive direction of the lines of force passing in 
its neighbourhood (or, in other words, in the direction, as 
nearly as may be, in which a magnetic needle would point 
if pkced in its neighbourhood). A body which becomes 
magnetic in this way by the magnetic action of another 
body is said to be " magnetized '' by " induction. " We shall 
suppose, in the meantime, that it loses all the magnetism 
thus acquired when the inducing action is withdrawn; 
although this is not necessarily, and in fact not generally, 
the case, as we shall see by and by. The reason why soft 
iron is attracted by a permanent magnet is therefore now 
said to be that the iron becomes magnetic by induction, 
and is then acted upon by the magnet like any other 
magnet similarly placed. The accuracy of this analysis 
of the phenomenon may be confirmed by many simple but 
striking experiments, such as the following. 

In ^e experiment above described, instead of placing 
the non-magnetic bar in a horizontal plane, place it in the 
plane of the magnetic meridian with its axis in the direc- 
tion of the earth's force (/.e., parallel to the line of dip). 
The lower end of the bar will then be found to repel and 
the upper end to attract the north pole of the needle 
(figs. 9, 10). This is at once explained on the above 
bypothesb ; for the bar will be magnetized inductively by 
the earth's force, so that its lower end becomes a north 
pole, and its upper end a south pola 



Let NS (fig. 11) be a bar magnet placed horizontally 
so that its axis produced passes through O, the centre of 
suspension of the needle sn, then the needle will be deflected 




Fig. 9. 

in the direction of the arrow. If now we place between S 
and O a small sphere of soft iron, this deflexion will be 




S 



Fig. 10. 

increased, the reason being that the sphere is magnetized by 
induction, having a south pole towards O and a north pole 



N 






-o--- 




/' 



Pig. 11. 

towards S, and the action of these is added to that of NS. 
Let NS (fig. 12) be a magnet placed in the magnetic 
meridian, n's a small , , 

magnetic needle in the — - ^ ■ f - 

same horizontal plane, 
with its centre in the 
line bisecting NS at 
right angles. When 
acted on by NS alone, 
n's' will place itself 
parallel to NS, with 
its north pole pointing S^ 
in the direction NS 




Fig. 12. 

Let the dotted line represent a line of force If we mofe 
a small piece of soft iron ns along this line in the diiee- 
tion from N towards S, it will first deflect the needb •• 



MAGNETISM 



225 



in fig. 13, and fiiully u in fig. 11, and in each podtion 
raTeraing it end for end will not alter the efi'ect AH this 
ia at once explained by the above hypothesia. 

A variation of the last experiment may be mado thus. 
Place a magnet verti- „i 

cally, in Hie neigh- ^~~*~^' n 

bonrhood of a mag- 
netic needle ; bj mov- 
ing it up and down a 
poeitiou will be found 
in which the action of 
the magnet on the 
needle is wholly verti- 
cal, so that the needle ^L 



=In 



Fig. 13. 




is not deflected from 
the magnetic meridian. 
Now take a small piece 
of soft iron and move 
it along a line of force 
passing near the needle, 
proceeding from the 
north to the south 
pole of the vertical 
magnet It will then 
be found, in accord- 
ance with our hypo- *'* 1*- 
thesis, that the north pole of the needle is first repelled, 
and finally attracted by the eoft iron. 
'■ If we hang two short pieces of iron wire alongside of 
each other by parallel threads, they will be found to repel 
one another, and to 
hang separated by a 
considerable interval 
when a magnet is 
brought under them 
(see figs. 15 and 
16). This experi- 
ment is dne to 
Gilbert, who rightly 
explains it by saying 
that the two ends 
nearer the magnetic 
pole S become like 
poles of opposito 
kind to 8, while the 
two farther ends are 
like poles of the 
same hind as S. The 
experiment may be 
varied by placing 
eome little distance 
below the pole of a 
magnet S a piece of '^.-^^^v, 
mica or thin card- Fig. 15. Pig. 18. 
.board M, and placing below that a short piece of soft iron 
wire; it will remain adhering to the mica, and so long as it 
is alone will hang more or 
lees nearly vertical, but when 
another ia placed aloDgside of 
it the two will diverge as in 



. 17. 



■I- One of the moat interesting 

■ examples of magnetic indue- M 

5"" tion is furnished by the action 

of a magnet on iron filings. 

If we plunge a magnet into 

a quantity of iron filings 



TT 



3M 



Fig. 17. 
and then remove it, we find it thickly fringed around the 
poles, where the filings adhere to the magnet and to one 
another so as to form abort bushy Glamente ; the Uiick- 



nees of the fringe diminishes very nipidly towards the 
middle of the magnet, where very few atUiere at all. Theae 
filaments are composed of magnetized particles of iron 
adhering by their unlike poles. 

If we place a small bar magnet under a piece of mode- 
rately rough drawing paper, strewn as nnifoimly as posdble 
with fine iron filings, and then tap the paper very gently so 
as to relieve the friction, and allow each filing to follow the 
magnetic action, then the filings will be seen to arrange 
themselves in a series of lines, passing, roughly speaking, 
j from pole to pole, as infig. 4 (p 223). The ezplauationof this 
phenomenon ie simply that each filing becomes magnetized 
by inductioo, and, if it were quite free to move about its 
centre, it would not be in equilibrium until it set its longest 
dimension along the line of force through its centre. The 
roughness of the paper effectually prevents translation, but 
does not hinder rotation, especially when the friction ia 
relieved by tapping ; hence every filing does actually set as 
if it were a little magnetic needle, subject of course to 
some slight disturbance from the neighbouring filings. The 
whole therefore assumes a grained structure, and the 
graining runs in the direction of the lines of force. We 
have thus an extremely convenient way of representing 
these lines to the eye, which lends itself in a variety m 
ways to the illustration of magnetic phenomena. In fig. S 
are shown the lines formed in the field near two like 
magnetic poles. These magnetic figures may be fixed in a 
great variety of ways, and projected on a screen so as to be 
visible to a. large audience, but it b scarcely necessary to 
dwell here upon details of this kind. 

These magnetic curves seem to have fixed the attention 
of natural philosophers at a very early period. They were 
originally called Uie magnetic carrents, from an idea that 
they represented the stream lines of magnetic matter, which 
explained the magnetic action according to the theory then 
in vogue. La Hire mentions them, Mem. dt PAead., 1717. 
Bazin gives an elaborate account of them in his Deteriptioit 
da Courant J/agnetiqwi deuinis d!apri» Nature, Stras- 
bnrg, 1753. Musschenbroek seems to have been the first 
to give the correct explanation depending on magnetic 
induction, Diu. de Mantle, 1739. 

If the filings be laid very thickly on the paper, and one Lqcts- 
pote of the magnet be brought under them at a short tlu'a «- 
distance off, they will arrange themselves in a pattern, P*'*""*"*- 
and at the same time bristle up so as to stand more 
or less erect, according as they are nearer or farther 
from the magnet. They have thus the appearance of 
being repetltd from the magnet It was, in all proba- 
bility, this phenomenon that was observed by Lucretius 
when he says (vL 1042): — 

"EiutUre etUm Samothracia t«rrfa vidi. 
Ac nmcnta simul ferri furera iDtns *h«nis 
In sciphiis, lipis hie Maguei cam anbditiu ttati." 

His conclusion, therefore, that iron sometimes flies and 
sometimes follows the magnet, was scarcely justified by his 
experimental facts, and it ia a mistake to suppose, as some 
have done, that he was aware of the polarity of permanent 
magnets. 

If we tap the card in the last experiment a curiotu Hsgiwtic 
result may sometimes be observed.' The lines (dfUdax. 
filings will be seen to reetde from the point of the card 
Immediately over the pole of the magnet If, however, the 
magnet bo held over, instead of under, the card, tapping 
will cause the filings to approach the point under the pole 
of the magnet The most probable explanation ^ of this b 
to be found in the fact that the erected filings stand in the 



■ ^plnns, Tentamen Tlttorim EUctricitatit tt Magiittimii,\\^% ■ 
CsTslto, TreatiMBn Magnetitm, 1787. ' 

* Roget, LOrarf of Umfid Knovltdge, 1632. - 

XV. - > . 



226 



MAGNETISM 



former case as shown in fig. 18, and in the latter as 
shown in fig. 19 ; that is, in both cases, owing to the action 
of gravity, they are more acately inclined to the card than 



,^ 



./ 






n/ff 



Fig. 18. 

the lines of force (represented by dotted lines in the figure). 
Consequently, when the filing springs up into the air, and 
is thus free to follow the magnetic couple, it turns more 




Electro- 
magneta. 



Induced 
and per- 
manent 
magnet- 
ism in 
the same 
l)ody. 



Fig. 19. 

into the direction of the line of force ; the effect of this is 
to carry its lower end each time a little farther from 
the axis of the magnet in the one case, and a little 
nearer to it in the other. 

By far the most important case of magnetic induction 
is the electromagnet. Whenever an electric current flows 
in a closed- circuit, the surrounding space becomes a field 
of magnetic force, and any piece of iron in it will be in- 
ductively magnetized. Such an arrangement of an electric 
circuit and iron is called an electromagnet The variety 
of form and of application of such instruments in modem 
science is endless. A few of the more important modifica- 
tions will be considered below. 

Coexistence of Induced and Permanent Magnetism. — The 
fact that a body is already a permanent magnet does not 
prevent its being susceptible to magnetic induction. If 
we take any piece of iron at random, the chances are that 
one end or other of it will repel the north pole of a magnetic 
needle, — in other words, it will be to some extent per- 
manently magnetic ; but if we bring it slowly nearer and 
nearer to the pole of the needle, provided its magnetism be 
not too strong, it will by and by attract the pole which it 
at first repelled. Again, if we take two steel magnets, 
which may be as powerful as we please, provided at all 
events that they are unequally powerful, and bring two like 
poles together, these poles will at first repel each other in 
accordance with the fundamental law of permanent magnets ; 
but, when the distance is less than a certain amount, the 
repulsion passes into an attraction, and when the poles are 
in contact this attraction may be very considerable. These 
phenomena are at once explained by the law of induction. 
The induced or temporary magnetism is superposed on the 
permanent magnetism, and, when the poles are near enough, 
the opposite magnetism induced by the pole attracts it 
more than the permanent like magnetism repels it ; and 
this happens even with steel, whose susceptibility for 
magnetic induction is considerably less than that of iron. 
This phenomenon was observed pretty early in the history 



of magnetism, but was not fully explained until the idea of 
magnetic induction was fully developed. Michell, in lus 
Treatise of Artificial Magnets^ gives a tolerably clear 
account of it. Musschenbroek mentions it,^ along with the 
fact that a magnet attracts iron more than it does another 
magnet, but offers no explanation of either fact The latter 
result, so far as it is true, can of course be explained by 
the smaller susceptibility of steel, particularly of hard 
steel, to magnetic induction, which is the main factor in 
attraction at small distances. Poggendorff' and others 
have experimented on the subject in later times. The 
reader should notice the close analogy between these 
phenomena and the repulsion and attraction at differeut 
distances between two similarly electrified condactois. 
See article Electricity, vol. viiL p. 33. 

Induction of Permanent Magnetism, — The case above 
supposed, in which the induced magnetism is wholly 
temporary, although it can be easily realized with small 
magnetizing forces, is not the general one, but in fact the 
exception. Usually a certain proportion of the magnetism 
remains after the inducing force is removed. This happens Coot 
even with the softest iron, when the inducing force is veiy^<"^ 
great Just as bodies differ very much in their suscepti- 
bility for induced magnetism, so they differ greatly in their 
power of retaining this magnetism when the inducing force 
ceases, or, as the phrase is, in "coercive force." Thus, while 
the inductive susceptibility of steel is less than that of iron, 
it retains much more of the magnetism imparted to it, 
and is therefore said to have much greater coercive force ; 
and the coercive force is greater the harder the steel is 
tempered. 

It is obvious, therefore, that the principle of " induction,'' 
along with the idea of "retaining power" or "coercive force,* 
furnishes us with the key to the explanation of the com- 
munication of permanent magnetism, whether by means of 
natural magnets or of artificial magnets, or of the electric 
current In particular, we see at once the reason why the 
end of a needle which has been touched by the north pole 
of another magnet becomes a south pole, and vice versa^ — a 
fact which greatly puzzled the earlier magnetic experi- 
menters, and indeed all who were inclined to think that, in 
the process of magnetization, something was communicated 
from the one magnet to the other. 

Mathe3iatical Theory of the Action of Perma- 
nently Magnetized Bodies. 

In this section we shall suppose the bodies considered to 
be rigidly magnetized ; Le,^ we shall suppose that magnetic 
action exerted on any body produces no change in its 
magnetization. It is further to be observed that we are 
merely establishing a compendious representation of ob- 
served facts, and foreclosing nothing as to their physical 
theory or ultimate cause. Our method is therefore to 
some extent tentative, and its success is to be judged by 
the agreement of the results with experiment 

There are two main facts to be borne in mind >— (1) that 
a magnet is polarized, and (2) that the properties of its 
smallest parts are similar to those of the whole. Adopting 
the mathematical fiction of action at a distance, we may 
represent the action of such a body by a proper distribntioa 
of imaginary /xmVtt;^ and negative attracting matter throngb- Foitt' 
out its mass. This imaginary matter, following Sir W. ^ 
Thomson, we shall call "magnetism," as we thns avmd 
suggesting other properties of matter than attractioii, ol^ 
which in the present case experience has given no eridenee. 
We assume that magnetism of any sign repeU magnetitm 

^ Cambridge, 1750. 

s PhUowphia NaiwaUs, %% 958, 954, 1762. 

* Pogg. Afm,^ xlv. p. 875, 1888. 



MAGNETISM 



227 



of the Kimt sign andaltraOa magi^etUm of the oppotite sign. 

Magoetum is suppoeed to be so associated with the matter 

of the body that magoetic force exerted on the magnetiam 

is ponderorootive force exerted on the matter. Oa the 

other hand, magoetic force is always supposed to be exerted 

by magnetism upon magnetism, and never directly by or 

upon matter. Into the natnre of this aasociation of 

magnetism with matter there is no pretence, indeed no 

need, to enter. 

1- The elementary lav of action assumed is that the attrac- 

* tion or rfpuUian (a» the caie may be) between tvro quanfitiei 

'" M and m' of magnetiimiuppoied concentrated in tvio point* at 

*■ a dittance r apart it -^' and is in tke line joining the (ico 

f point*. This supposes that the unit quantity of magnetbm 

'* is BO chosen that two units of positive magnetism at unit 

distance apart repel each other with unit force. This 

definition, which is fundamental in the electromagnetic 

system of units, gives for the dimensions of a quantity 

of magnetism [L'M*T~^]. If the electrostatic system be 

adopted the result would of course bo different 

th An accurate meaning can now be given to the phrase 

f- " strength of a magnetic field," or its equivalent " resultant 

magnetic force at a point in the field ; " it is defined to 

I be the force exerted upon a nnil of potilive magnetism 

tie tuppoted concentrated at the point. The force exerted on 

a unit of negative magnetism would of course be equal in 

magnitude, but oppositely directed ; and in general, if R 

denote the resultant magnetic force at the point, the 

magnetic force exerted on a quantity k of magnetism 

concentrated there is kR. 

u We may, as in the corresponding theory of electricity, 

introduce the ideas of volume density (p) and surface 

' density (o-), — so that fxh and o^S denote the quantities 

1. of magnetism in an element of volume and on an element 

I. of surface respectively ; p and <r may of course be positive 

or negative according to circumstances. 

It will now be seen that, mathematically speaking, the 
theories of action at a distance for electricity and magnetism 
are identical, and every conclusion drawn will have, so far 
as the physical diversity of the two cases may allow, a 
double application.^ In particular it will be found that 
the theory of magnetism, when properly interpreted, gives 
the theory of dielectrics polarized in the way imagined by 
Faraday. 

The fact of magnetic polarity requires the conception of 
'*' negative as well as positive magnetism ; the fact that the 
"** properties of the smallest parts of a magnet are similar (o 
those of the whole requires that in every element of the 
body there shall be both negative and positive magnetism. 
From the fact that in a uniform field, i.e., ova in which the 
resultant magnetic force has at every point the same 
magnitude and direction, the force of translation upon a 
magnet is nil, it follows that the algebraic sum of all the 
magnetism in any magnet must be zero ; for, if R denote 
the strength of the field, by the theory of parallel forces 
the whole force on the magnet will be S(kB), = RSk ; 
hence Sx = 0. In other words, in every magnet there mutt 
be (I* mveh negative at positive magnetism ; and this con- 
clusion also must be extended to the smallest parte of every 
magnet, so long as we do not go behind the mere facts of 
observation. The positive and negative magnetism cannot 
be coincident throughout, otherwise there would be no 
external magnetic action, but the separation is in the 
elements of the body. lliuB, although ther« is no force 
of translation in a uniform field, there will in genenl be 
a couple. Consider the positive and negati 



separately, aud let k denote any element of the former and 
k' any element of the latter. Let N be the centre of mass 
of the positive, S the centre of mass of the negative 
magnetism ; so that, if the magnet be referred to a set of 
rectangular axes, the coordinates of K and S are 



and 



fi). 



Let the distance KS-/, and let K-fS<c,- -I^k; this 
quantity K is called the "magnetic moment" By the theory 
of parallel forces, if we suspend the magnet in a uniform 
field of strength R, the action upon it reduces to two forces 
R2k and - RSk, each parallel to the direction of the field, 
acting respectively at N and S, in other words to a couple 
whose moment is RSxfsin;^ or KRsin^f, where ;f 

angle between SN and the direction of the field. Hence, & 
if the magnet be perfectly free to follow the magnetic action 

of the field, it will set so that the line SN or the line NS 
is parallel to the direction of the field, the equilibrium 
being stable in the former case, but unstable in the latter. 
The line NS is therefore parallel to what we have already 
defined on experimental grounds as the axial direction in 
the magnet N, S, and NS are sometimes called par 
excellence the poles and the axis of the magnet ; we have 
adopted the looser definition given above because it is more 
convenient and nearer the popular usage. 

Tbe above resnltt mny be npplie<l to soma cum very imnortiut ioTl 
praotics. L«t the mafjnet whose centrea ot positive and nentive o( 
macnetism are N and S be saspcnded bv the middle point of NS, di 
wliioh, for simplicity, may be assumed to be also its centre of m 
gravity. Let OX (fig. 20) b« a horizontalline drawn northwards, OZ 



Magneto 
couple in 
nniloim 




ni«^eti( 

insU 9 with the magnetic 
meridian, an^ Irt ON m'ako an aiij:;1e f n-ith the horiion. IlB be 



the vertical jilane through NS make 



;th of the earth's niaffnelic 
H-Rca«aDdZ-Rsi 



then the horizontal and vi 



' To prevent needleu repetition, we shall adopt henoefoith, irithont 
fortlier explanation, the deflaitloni, terminology, and Tstnlt* given In 
th* aitid* £LicTuciTr, voL vUL p. M «{. 



2. 3j(. R cost— coa^aintf, or KRcosicos^sinS. 

In other words the directive couple varies as the sine of 
the angle of deviation from the magnetic meridian. This 
conclusion was verified experimentally by I^mbert, and 
also by Coulomb^ by means of his torsion balance. It 
will be seen that, rscteris paribus, the directive couple is 
greatest when the magnetic axis is horiiontal 

■ Mitn. de {A<ad., 17W. 



228 



MAGNETISM 



Next suppose the angle fixed, and the macnet free to rotate 
about a horizontal axis inclined at an an^le 90 - 9 to OX. The 
couple tending to diminish the angle ^ is ER(cosi cos9 sin^- 
sini cos^). The position of equilibrium is given by the equation 
tan ^— sec 9 tan i. 

The angle at which the axis is depressed below the 
horizon is therefore least when ^ = 0, and greatest when 
^=s90% its value being i in the former case, and 90° in 
the latter, as stated above, p. 221. 

In general, if x', /i', v' and A, /i, y be the direction cosines of the 
direction of the field and of the axis of the magnet respectively, then, 
resolving the forces acting at N and S, we see at once that the three 
components of the magnetic couple are 



KR(i//i-MH KRCaV - y'A), KR(/i'A-AV) 



(2). 



Magnetic 

moment 

TBMlved 

asa 

▼«ctor. 



Finite 
magnet 
replaced 
by an 
infinite 
nnmber 
of in- 
finitely 
amall 
magnets. 



Intensity 
of 

magnet- 
iation. 



These are clearly the same as the components of the couple on a 
system of three magnets whose axes are parallel to OX, OY, OZ, 
and whose magnetic moments are Ka, K/x, Ky. Hence, so far as the 
action of a unSbrm field is concerned, we may resolve the magnetic 
moment like a vector, and replace a given magnet by others the 
resultant of whose moments is the moment of the given magnet. 

It appears therefore that in a uniform field every magnet 
behaves as if it were made up of a certain quantity of 
positive magnetism and an equal quantity of negative 
magnetism placed at such a distance apart on a line 
parallel to the magnetic axis that the product of the 
quantity of magnetism into that distance has a value equal 
to the magnetic moment of the magnet. It is very im- 
portant to observe that the magnetic moment alone appears 
in the above formulae for the magnetic action. We can- 
not therefore separately determine from observations in a 
uniform field either the quantity of positive or negative 
magnetism in a magnet or the distance between the 
magnetic centres of mass. 

Let M be any magnet, and P a point whose distance from 
any point of M is infinitely great compared with the linear 
dimensions of M. Then, since all the lines drawn from P 
to different points of M are sensibly parallel and equal 
in length, we may suppose the positive and negative 
magnetism of M to be collected at their mass centres, i.e., 
M to be replaced by an ideal magnet. It is also obvious 
that, throughout a region around P whose linear dimensions 
are of the same order as those of M, the field due to M may 
be regarded as uniform. Hence we conclude that in cal- 
culating the mutual action of two magnets M and M' we 
may replace each of them by an ideal magnet, provided the 
distance between them be infinitely great compared with the 
linear dimensions of either. This condition may be satis- 
fied either by making the distance between the magnets 
very great if their dimensions be finite, or by making 
their dimensions infinitely small if the distance between 
them be finite. The second alternative suggests at once 
a method for representing the magnetic action of magnetized 
bodies at finite distances. We may divide up the body 
into portions whose linear dimensions are infinitely small 
compared with their distance from any point at which 
their action is to be considered ; each of these portions is 
itself a magnet, and may be replaced by an ideal magnet 
having the same axis and moment. The whole magnetic 
action is obtained by integrating the action of all the ideal 
magnets of which the body is thus supposed to be com- 
posed. 

Let X, fi, V be the direction cosines of the magnetic axis of 
any element dv of a magnet, and I such that Idv is the 
magnetic moment of the element, and let lA = A, I/x = B, 
Iv = C; then I is called the '^intensity of magnetization" at 
the point where the element is taken. I may be regarded 
as a vector which specifies the magnetization of the body ; 
in general it varies continuously from point to point ; if it 
has the same value and direction at every point, the body 
is said to be uniformly magnetized. A line drawn so that 
the direction of I at every point of it is tangential to it is 



called a '' line of magnetization.'' It is clear from what has lin« 
already been shown that we may if we choose replace the P^ 
element dv by three ideal magnets whose axes are parallel ^'^ 
to the coordinate axes, and whose moments are Adv, Bdv, 
Cdv respectively. 

If then E be the magnetic moment of the whole magnet, 9K the Beso 
moment of any element 9v, and />, g, r the direction cosines of the msgi 
axis of the whole magnet, we have K— 12k, — - 12k' ; and, remem- moa 
bering that k''^ -k for every element, and j 

(2kx 2/cV\1 ^(^*'"7~/ 



2(8Ka) SlASf SASp 



nK K K K 

We may therefore write, replacing summation by integration, 

Kp'^/f/Mv, Kq^/f/^v Kq^/f/Cdv . . (3). 

Let SN be an ideal magnet of infinitely small length 7, let m be iU Pota 
ma^etic moment, and iti^kI, Let Q be its middle point, and the of is 
angle PQN « 0, N being the positive or north-seeking pole ; and let finili 
QP« D. Then the potential at P due to this magnet is sbiI 

k[ DS-DZcose + ir'f'^-iclD^ + Dkos^ + JTS l"*. "^ 

Expanding and neglecting powers of -=-- above the firsts we get for 
the potential 



?;i cosO 
~I)«~ 



(1). 



Hence the potential at P (|, r;, o^ ^^ infinitely small magnet Potai 
Kdv at (x, y, z), having its axis parallel to the axis of or, iioffii 
-^ (C - ^)/i^*i aiid similarly for the other two. We therefore obtain nng> 
for the potential of the whole magnet 



y-^{Mi-x) + B{v-v)+C{(-z)}^dv 



-f/f\ 
-#■■ 



<-Jr) . /(i) . /(i) 



dx 
d 



+ B 
d 



dy 



— ^+C 



dz 



dv 



^rfi+'^d^ + '^ilii^^ 



(5). 



Taking the second of these expressions and integrating by parts 
in the usual way, we get 



dv 



where 



r— ^A+mB+nC — Icosa 
^^ /rfA rfB rfC\ 
"" \dx dy dz } 



(6). 



I, m, n being the direction cosines of the outward normal to any ele- 
ment d^ of the surface of the magnet, and B the angle between the 
noi*mal and the direction of magnetization at d&. 

Hence the action of any magnet may be represented by ^^^ 

means of a certain volume distribution (p) and a certain ^^ 

surface distribution (o-) of free magnetism. This important 

proposition is due to Poisson.^ 

The fact, in itself obvious, that the sum of all the magnetism of 
Poisson's distribution must be zero, gives the theorem 



Mi-f*i>'-#--B"<"'« 



-/A 



(7). 



I cos (23 



which admits of course of direct analytical proof. 

The magnet may also be replaced, so far as its external 9*°^ 
action is concerned, by a distribution wholly on its surface, ^^ 
as was shown by Gauss.^ This will be seen at once if we 
replace the positive and negative magnetbm throughout 
the body by positive and negative electricity, and suppose 
the surface of the magnet covered with a conducting layer 
in connexion with the eartL The surface will thus become 
charged with a distribution of positive and negative 
electricity whose total sum is zero, such that the potential 
of the surface is zero, and hence the potential at evety 
external point zero. The potential of this surface layer 

* Mim, de VInstiiut, torn, v., 1821. 

s Intemitas Vis, § 2 (1832), and Allgmeine LekmUu, % 36 (1839). 



MAGNETISM 



229 



MOf 

aoid< 
mag. 

0. 



at every point external to the body is therefore equal and 
opposite to that of the internal electricity. If, therefore, 
we change the sign of the surface density at every point, 
we obtain a surface distribution whose potential at every 
external point is the same as that of the body. There is 
of course only one such distribution : we may call it Gauss's 
distribution. 

Poisson's distribution will coincide with that of Gauss 
provided the magnetization be such that 

(8); 



dx dy dz 



mlt- 

;fofoe 

Kd«a 

KBBt* 



ic in- 

StiOIL 



when this condition is satisfied at every point of the body, 
A is said to be '< solenoidally " magnetized; a particular 
case is that of uniform magnetization. 

So long as the point considered is external to the magnet 
there is no difficulty in attaching a definite meaning to the 
resultant magnetic force (H) at a point ; its components 
are given by 

«--^' ^''Ty' ''"Tz ' • • ^^^' 

and the values obtained will be the same whether V be 
calculated by means of Poisson's or of Gauss's distribution. 
Inside the body the result is otherwise, for reasons that are 
not difficult to understand, when we examine the nature of 
our fundamental assumptions. It is therefore necessary 
to be careful to define what we mean by resultant magnetic 
force in the interior of a magnet It is defined by the 
above equation (9) on the understanding that V is calcu- 
lated from Poisson's distribution. We can show that S 
thus defined is the resultant force in an infinitely snuul 
cylindrical cavity within the magnet, whose axis is parallel 
to the line of magnetization, and whose radius a is infinitely 
small compared with its axis 25. 

The removal of the matter filling snch a cavity will affect 
Poi88on*8 volume distribution to an infinitely small extent ; the 
alteration of the force if any, will therefore arise simply from the 
surface distribution which we must pla(» on the walls of the cavity 
in order to make np the complete representation of the action of the 
magnet in the cavity. This distribution reduces to two circular disks 
of radius a at the two ends, the densities of the magnetism on 
which are - 1 an d + 1 r espectively. The action due to these is a 

force 4irl(l - ft/Va' + 6*) in the direction of magnetization. If a be 
infinitely small compared with 6, this force becomes zero, which 
proves our proposition. 

If, on the other hand, the cavity in the magnet be disk- 
shaped — say a narrow crevasse perpendicular to the line of 
magnetization — then the force due to the distribution on its 
walls becomes 47rl, and the resultant force in the cavity 
is no longer f|, but a force ^, whose components are 

a-a+4irA, 6-iS + 4irB, c-7+4irC . . (10). 

i! is called the '^ magnetic induction " at the point (.r, y^ z). 
From the definition of K it follows that outside the magnet 



Inside 



rfa 

dx 



+4«+4i_o (11). 

dy dz 



dx dy dz '^ ^ 



\ dx dy dz ) 



(12). 



n- 

uity 

i 

con- 

luity 

Sand 



At the surface of a magnetized body the tangential com- 
ponent of ^ is continuous, but the normal component 
increases abruptly by i^rlcosd in passing from the inside 
to the outside of the surface. 

Outside magnetized matter the magnetic force and the 
magnetic induction are coincident Inside we have 



da ^ de da 
dx dy dz dx 



dB dy 



--(S'f-f)-- <"^ 



dy dz 

Hence the magnetic induction satisfies the solenoidal con- 
dition both inside and outside magnetized matter. It has 
normal continuity, and, in general, tangential discontinuity, 
at the surface of a magnetized body. 



Snrfaos 

integ^rd 

of mag- 

netioUi- 

dnotiom 

U 



For if y, r and 9^ < be the normal and tangential components of 9 
and 1$ just inside, and t/, r' and n\ H the corresponding components 
just outside the surface near anv point, we have n — y + 4irl cos 9. and 
n'— y ; but 1^— y+4irIco89, therefore n'^iC, On the other hand 
t'=^, whereas t is the resultant of i and 4irlsin0, which is parallel 
to the surface, but otherwise may have any direction according to 
circumstances ; hence, since t'—^, in general r' is not equal to r. 

In fact there will be tangential discontinuity of the 
magnetic induction unless the line of magnetization be 
perpendicular to the surface of the magnet ; in this case 
there is complete contiouity of the magnetic induction. 
When the magnetization at the surface is tangential, there 
is, on the other hand, complete continuity of the magnetic 
force. 

It follows from the above that the surface integral of 
the magnetic induction taken over any closed surface S 
vanishea 

First, let the surface be wholly within or wholly without con- 
tinuously magnetized matter. We have, integrating all over S and 
all over the space enclosed by S, the analytics theorem 

hence the result follows, for every element of the right-hand integral 
vanishes. Next, suppose 8 to be partly within and partly without 
a magnetized body. Divide it into two parts by a double partition 
one of whose walls runs outside the surface of the body and 
infinitely near it, the other inside and infinitely near it ; then, on 
account of the normal continuity of % the surface integral will 
bo the same in absolute value over each of these walls. Hence the 
inte^^ over the whole of S differs infinitely little from the sum of 
the integrals over the two surfaces into which it is broken up by 
the douole partition, each of which vanishes by the former case. 
Hence the theorem holds in this case also. 

We may therefore apply to lines and tubes of magnetic 
induction without restriction all the theorems prov^ for 
lines and tubes of electric force in space free from electrified 
bodies. We may speak of the number of lines of magnetic 
induction instead of the surface integral if we choosa And 
we have this important theorem : — 

The number of lines of magnetic induction that past through 
an unclosed surface depends merely on its houiidary. 

There must therefore be a vector ^, whose line integral Veolor 
round the boundary is equal to the surface integral of ^ |^!^* 
over the surface. 

The components F, 6, H of ^ are connected with those of $ by 
the equations 



tiaL 



rt-^-^ 5.1^-^ .^?_^ 
dy dz * dz dx * dx dy 



(15). 



as has been shown in the article Electricity, vol. viiL p. 69. 

Mutual potential energy and mutual action of tico magnetic 
systems. — The potential energy of a small magnet is «r(V,- V,), 
where Yi and V,are the values of V at its negative and positive poles. 
If the magnet be infinitely small, of length ds say, the direction 
cosines of ds being A,ft,y, this may be written tcdsdyjaSy ue. , mdV/ds, 
or, if we are considering a magnetized element of volume dv, 

jf dV , dV rfVN, ,,.. 

^[^-^^^d^^'^-d^r ^^^'- 

Hence the potential energy of the whole magnetic system in a field 
whose potential is given 1^ V is 



Mutoil 
potential 
eneigy 
of two 
magnets. 



W 



-M 
-f/A 



^S^^i^^^^j^'' 



rfV ^rfV\ 



(17), 



(Aa+BiS + C7)rf» 



the integration being extended all over the magnetized masses sup- 
l)osed to be acted upon. Integrating by parts, we get at once 

\f^//Yffd%-vf//Yf^lv (18), 

ff and p being the surface and volume densities of Poisson's distri- 
bution, a result that might have been expected. W may alto be 
expressed as a sextuple integral ; for, if \\ \\ fi\ »•', a^, y, / refer 
to the acting system, then 



230 



Whence 



MAGNETISM 



[ ,i , ,d , ,<J\ 1 



(19). 



A remarkable expression for W may be obtained by supposing 
the integration in (17) extended throughout the whole of space, on 
the understanding that A, B, C are zero where there is no 
magnetized matter, and then integrating by parts. We get, since 

" ihc 



the surface integral at infinity may bo shown to vanish, 



(20), 



where it must be understood that A, B, C vary continuously, how- 
ever rapidly. In point of fact, where, as at the surface of a 
magnetized body, there is discontinuity, a finite portion of the 
integral will arise from an infinitely thin stratum near the surface. 
The proper representation of this part will be a surface integral, as 
may oe seen by referring to (18), from which we might have started. 
If now y be the potential of the magnet acted upon, then 






whence 



rf^' rf2V' fdk rfB rfC\ . 
"*■ rftr» dz^ ""Vrfa; "^rfy "^ dz) * 

jdv 



^-hms*^ 



W dz^ 



" 4irjC^ \dx dx dy dy dz dz ) 



RR'cos^rfr 1 



(21), 



where R and R' are the resultant forces at any point of space due to 

the acting and ucted-upon systems respectively, and B the angle 

between their directions. 
Foroe In practice W is expressed as a function of the variables (equal In 

and naml]«r to the degrees of freedom) that determine the relative 

ooaple position of the two systems ; difierentiation with respect to any one 
on a of these then gives the generalized force component tending to 
magnet decrease that variable. 

in given We may also calculate the forces directly. For, the components 
field. of force on the element dv^ being the diflerences of the forces acting 

on the two poles of the clement, arc 



(4'-4;+cg>.'o-' 



and the components of conple, in calculating which the field may 
be supposed uniform, are (see above, p. 228) 

(7B - $C)dv, &c. 

Hence, integrating, we get, with the chosen origin, for the com- 
ponents of tne whole force and couple, 

and similarly for g and %, 
I-^|,B-,C.,(igtB|+0|) 

and similarly for IS and |t. 

In the important case of a uniform field whose components are 
a, iS, 7, we have 

.... (23), 



-<Ag.B^^.C' 



(22). 



W--K(;o + miS+n7) 



K being the moment of the maffnet, and Z, m, n the direction cosines 
of its axis. From this formula the results given above (p. 227) can be 
deduced with great ease. 

Examples, — Some examples of the application of the 
foregoing theory are here given, partly on acconnt of their 
intrinsic value as types enabling ns to conceive the differ- 
ent varieties of magnetic action, partly for the sake of the 
light they throw on the theory itself. The reader who 

« See Thornton, RepHni of Paper$ on Electricity and Ua^etitm, p. 4S«. 



magneti- 
xatioB. 



desires more sach should consult Maxwell's Electricity 

and Magnetism^ or Mascart and Joubert, Le^iu gur 

VElectridte et le Magnetisme, 

SoUnoidal Magnets have already been defined as such that the S:>le- 
vector I satisfies the solenoidal condition ooidil 

rfA rfB^rfC^Q 

dx dy dz" ' 

The lines of magnetization, therefore, have all the properties of 
lines of magnetic induction or electric force. In particular, if we 
consider a portion of the magnet enclosed by a tube of the lines of 
magnetization, the product of the intensity of magnetization by the 
section at each point is the same. Such a portion of magnetized 
matter taken by itself is called a ** magnetic solenoid," and the pro- 
duct mentioned is called its ' ' strength. It is clear (from the general 
definition, or it may be proved directly from the secondary property 
just mentioned) that the action of the solenoid may be represented 
by the distribution of a certain quantity «I of positive magnetism 
on the one end and an equal quantity of negative magnetism on 
the other, I being the intensity of magnetization, « the normal sec- 
tion at the end. The action thcreforo depends merely on the 
strength of the solenoid and on the position of its ends. The shape 




pitr 



21. 



of the intervening poi-tion is immaterial. If we suppose it straight, Eqoip 
and if the section be infinitely small so that the magnetism at the tentia 
ends may be regarded as condensed at two points, we have an ideal linei i 
magnet of finite length. The equipotential lines of such a magnet linet < 
in any plane through its axis are ot course given by the equation force. 

____« const (24), 

where r and^/ are the distances of any point P on the line from the 
poles. 

The equation to the lines of force is easily obtained ; ' for, if KP Ideil 
and SP (fig. 21) make angles $ and 6^ with the axis of the magnet, bar 
and ^ and ^' with the line of force, we must have magu 

sin ^/r^ - sin ^'/t^^ ; 
hence, since 

Bin ^t-^rdB/ds, sin^'— /rf^/dlf, 
we get 

dB/r-dB'/r^^O; t.e., sine rfe- sin e'rf^'-O ; 

which gives for the equation to a line of force 

cos 0- cos ^« const (25). 

We may imagine a magnet of this kind so long that the action Tvo 
of one of its poles may be altogether neglected at points which are like 
at a finite distance from the other. We thus effectively realize what polai. 
never occura in nature, viz., a magnet with one pole only. If we 
place the like poles of two such magnets near eacn other, we get a 
neld the equipotential lines and lines of force in any axial plane of 
which are given by the equations 

^ f4--const . (26). 



r / 
COS0+ cos^—const (27). 

The lines of force given by ea nations (25) and f27) may be traced 
in a diagram by means of the following simple and ele^nt conatmc- 
tion.' Draw two circles A and B, having equal radii and N and S 
respectively for centres; produce the line NS both ways, and, 
starting from the centre, divide it into any number of equal parts ; 
through these draw perpendiculara to meet the circles A and B ; 

s The flnt mathematical inrestigations of the eqnatioo to the llnet of force of 
an ideal magnet appear to have been made bj Playf air at the reqmat of Bobteoa. 
and bv Leslie, Oeom. Analysis, 1821. They had prerionalj been vwy earefnlhr 
comldered from an experimental point of riew hj Lambert, if<An. die f ilMA m 
Berlin, 1766. 

* Roget, Jotir. Roy. Tnsf., IftSl. 



MAGNETISM 



231 



firom N draw k MiieB of Iidgb U 

bom S a liiiiilsr series to the p ^ ^ . . 

will form a network of lozengea the loci of the verticea of which methods. In fact, by proper arrangemcDt, every problem in the 
will be lines of force, corresponding to (25) or (27} According u we I one subject can be conrerted iuto > problem in the oth«r. For 

details we refer the reader to Thomson, who was, so far as we know, 
/ the first to work out this matter fuUy ; in the present connezloB 
le should consult more particularly gj C7S sq. of the Stprinl, 




Fig. 22. 

pass from point to point along one set of lozenge diagonals or alone 
the other. Fig. 22 will pM the reader an idea of the geDeral 
appearance of the two sets of lines. He may compare the ideal with 
the actnol cases by referring to figs, i and 6, p. 222. 

In the cose of an infinitely smallniagnet, the equipotential lines are 
of course given by the polar equation t^ — e'coaS, e being a variable 
parameter. It is easily shown that the lines of force, which are 
t necessarily orthogonal to these, have for their equation r — « ein'f.' 
If # be the angle between r and the tangent of the line of force, we 
hare tanf — rrf»/ifr — 1 ton* ; hence the following construction for 
the direction of the line of force at F due toasmoll magnet at O: — 
let K be the point of trisection of OP nearest O, and let KT, per- 
pendicnUr to OP, cut the aiia of the magnet in T ; then TP is the 
tangent to the line of force at P. This construction in a slightly 
diBennt form was given by Hansteen * and by Qauss ' ; t he latter 
adds that the resultant force at P is given by M.PT/OT.OP* where M 
is the maonetic moment of the magnet, a proposition which the 
reader wilfeasily verify. These propositions ore of considerable use 
in rough magnetic calculations. As this is an important case we 
give a diagram of the equipotential lines and lines of force in 
gg. 23. 

We may, if we choose, condder a filament of matter magnetized 
longitadinally at every point, but so that the atrength vl(— J, aay) 
is variable. Such a filament is calletl a complex solenoid. It may 
clearly be snpposod made np of a bundle of simple solenoids whose 
ends are not nil coincident with the ends of the filament. If di be 
•n element of soch a filament, the potential is given by 

That is, its action may be represented by two particles of 
magnetism J, and J, at its two ends, and by a continaotis distribu- 
tion of free magnetism along its length whose density is -dJ/dt. 
This is of course merely a particular case of Poiaun's distribution. 

When a body is solenoidally msgnetiied, the magnetic force 
9 both external and internal depends solely on the surface distri- 
liution, i.t., merely on the ends of the solenoidi of which the body 
i« eompoaed. We may therefore soppoee the two ends of any 
•olenoid joined by a solenoid of equal strength Ifing In the mrTsce 
of the body. Proceeding thus, we may in an infinite number of 
ways constmct a sarface layer of langeniiaily magnetiied matter 
which will lepresent the magnetic action of a solsnoidally 
magnetiied body. Thomson has shown by means of a highl^ 
intereatins piece of analysis how to find the components of this 
tangent) J^msgnetiiation. 9ee Seprint of Pi^ieTM on ShttrMtyand 
Moffi^iim, p. 101. 

Tlie magnetic theorems jnat stated will suggest at once to the 



Uniformly ita^nttUrd Bodia constitute in practice the moat im- Potential 
portant case of oolenoidal magnets. In the Gnt place it is obvioni of oni- 
that the whole mognetic moment of such a body is simply ita volume formly 



'oisson's method 
this case merely from a 
surface distribution of vary- 
ingdensity Icoeft We may 




I HuutacB, UaoHHtmiu 4w ErA, p. »• ( 

• MogmrtUmMi dfr Brd,, p. Me. 

■ «mbMM) *. Hi. nnAH, INT and IHO. 



ing normal thickness. Let 
the thickness at any point 
measured parallel to the 
magnetic axis be ( ; then 
the normal thickness is 
hence fl cot B— 



fore suppose the magnet I 
replaced by itself (fig 21) ^ 
with a uniform volume 
distribution p of positive 
magnetism, and itwlf dis- ''B- "-*■ 

placed through a distance 1 in a direction opposite to that of 
magnetization with a uniform volume distribution -p; or, which 
comes to the some thing, the potential of the magnet at P is 
o(U-U'), where U is the potential at P of a uniform volume distri- 
bution of density -t- 1 throughout the magnet, and V the potential 
of the same at a point V displaced through a distance t in the 
direction of mognetiEBtion. 

If I, nt, n be the direction cosines of the magnetic oxii^ this gives 



./■/fU^ rfU dV\ 



where X,T, 
disttibniior 
of the 



The same molt may also be arrived at thns. The part of tlw 
potential due to the element dv it Idt coa t/r*,